On the issue of rebirth:

The Buddha taught causality, especially the causality of mental processes. He used inchoate verbs to point to key areas in the causal process: verbs like becoming and birth. He pointed to beginnings because that’s where we can have some influence and control—ending and death are less cooperative. Endings are useful only as a way to measure skill.

Beginning and birth, ending and death, are simply points in causal processes that we are able to focus our attention on. Everything is inconstant. Continuity is a delusion. Rebirth is an incoherent concept.

One noted teacher says the Buddha didn’t use the word “rebirth”, he said, “further becoming” (unskillfulness causing more becoming). Maybe that was the Buddha's way of sidestepping any discussion of the afterlife, something his Handful of Leaves teaching seems to imply he wouldn't have tried to teach (or disprove).

If we want freedom from suffering (nirvana) and infinite happiness (buddhahood), then certainly it matters if there is rebirth or not.

In another sense, I can do something much more efficiently if I have comprehensive knowledge. Thus, it is relevant whether there is rebirth or not.

These are (just) 2 reasons why it the question of rebirth matters.

There is a collection of buddhavacanna (words of Buddha) titled "Jataka Tales". They are stories of BUddha's past lives.

Then one of the most important concepts in Buddhism is dependent origination (the 12 links). The way it is presented by Madhyamika school is that a single wheel (wheel of life a.k.a 12 links of dependent origination) require a minimum of 2 lives to be explained properly.

Then Acharya Dharmakirti presents an argument establishing the logical validity of past lives.

I have mentioned 3 facts which should serve to make you reconsider your statement that the Buddha says there is no past life or that it is a way [I am merely paraphrasing of course] of taking about living, as a survival thing.

My penultimate point will be about the problem of karma, as you have mentioned, in its 'psychological flaw'. I only mention here that while we are using the same word (a label, a referent) what AND how Buddhists and non-buddhists understand is quite different. (Not to of course ignore the similarities or much more importantly besmirch a great tradition such as it is).

The final point is with respect to the icocnic phrase of Marx "opiod of the masses". With all due respect to the briliant intellectual, and pragmatic, Marx (whom I admire as a thinker, irrespective of what ideas I agree or disagree with); his understanding of Buddhism is incorrect. 2 reasons should suffice to bring home the point. First, the end goal of Buddhism is liberation. Liberation from what? One of the answers to this what is bondage, freedom from illusion like world. Opiods do, very generally speaking, just the opposite. Second, the way Marx uses religion is much more in line with Abrahamic religions. Coneptually, buddhist does not fit into a categorization of a different conceptual scheme.

I hope this clarifies something.

Karma (by its nature) is cyclic and repetitive. Think of it like waves: the momentum of a crest creates a fall and produces a trough; the momentum of a trough creates a rise and produces a crest. Is it the same crest?

Hmph.

The eponymous self is a collection of forms — physical forms, emotional forms, mental forms — and these forms all have their own momentum. At any given moment they might seem like something solid and immutable, but that's just a trick of the thinking mind, the way we see a wave roll across the ocean without considering that the water barely moves at all. So if all the forms of this eponymous self fall apart and come together again, what is that? A body breathes in and a body breathes out; is it the same body? A self goes to sleep at night and a self wakes in the morning; is it the same self?

Again, hmph.

We think too much about existences and not enough about momentums. What cycles are producing us? What are we setting in motion? What will be reproduced in our wake? Liberation is all about momentum: about seeing it and guiding it and stilling it.

TL;DR

Denying rebirth-of-self view while clinging to self view is wrong view, because this is annihilationism and brings the unenlightened to hedonism.

Denying rebirth-of-self view after discarding self view is the noble right view. Rebirth without self view is simply the continuation of suffering and the continuation of the chain of conditioned processes. It's not about the rebirth of a specific person or being or self or consciousness.

Rebirth view can be used as skillful means (upaya) to remove the habit of misconduct, cultivate virtue and generate the path to liberation. Rebirth view is the middle way and is the right view with effluents/ taints.

Please also see this answer.

Long answer

Denying rebirth-of-self, while clinging to self-view, appears to be wrong view. This is unskillful means because it directs the mind of the unenlightened towards hedonism and nihilism. This is also the view of annihilationism.

And what is wrong view? 'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no contemplatives or brahmans who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is wrong view.
MN 117

Holding on to the rebirth-of-self, while clinging to the fetter of self view, is a right view with effluents/ taints.

"And what is the right view with effluents, siding with merit, resulting in acquisitions? 'There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions. There is this world & the next world. There is mother & father. There are spontaneously reborn beings; there are contemplatives & brahmans who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is the right view with effluents, siding with merit, resulting in acquisitions.
MN 117

Why is this the case? This is because siding with merit, one could use this as skillful means (upaya), a helpful tool, to remove the habit of misconduct, cultivate virtue and generate the path to liberation.

The Buddha is the doctor (Iti 100) who treats the illness which is suffering (dukkha). This is a medicine that he has prescribed.

“And for the sake of what benefit should a woman or a man, a householder or one gone forth, often reflect thus: ‘I am the owner of my kamma, the heir of my kamma; I have kamma as my origin, kamma as my relative, kamma as my resort; I will be the heir of whatever kamma, good or bad, that I do’? People engage in misconduct by body, speech, and mind. But when one often reflects upon this theme, such misconduct is either completely abandoned or diminished. It is for the sake of this benefit that a woman or a man, a householder or one gone forth, should often reflect thus: ‘I am the owner of my kamma, the heir of my kamma; I have kamma as my origin, kamma as my relative, kamma as my resort; I will be the heir of whatever kamma, good or bad, that I do.’ .....

“This noble disciple reflects thus: ‘I am not the only one who is the owner of one’s kamma, the heir of one’s kamma; who has kamma as one’s origin, kamma as one’s relative, kamma as one’s resort; who will be the heir of whatever kamma, good or bad, that one does. All beings that come and go, that pass away and undergo rebirth, are owners of their kamma, heirs of their kamma; all have kamma as their origin, kamma as their relative, kamma as their resort; all will be heirs of whatever kamma, good or bad, that they do.’ As he often reflects on this theme, the path is generated. He pursues this path, develops it, and cultivates it. As he does so, the fetters are entirely abandoned and the underlying tendencies are uprooted.
AN 5.57

Once self-view is discarded, rebirth-of-self view will also be discarded. This is the noble Right View.

"And what is the right view that is noble, without effluents, transcendent, a factor of the path? The discernment, the faculty of discernment, the strength of discernment, analysis of qualities as a factor for awakening, the path factor of right view in one developing the noble path whose mind is noble, whose mind is without effluents, who is fully possessed of the noble path. This is the right view that is noble, without effluents, transcendent, a factor of the path.
MN 117

How do we know that rebirth-of-self view will be discarded? This is the higher teaching for those who have understood anatta, as taught in MN 38 and SN 22.85.

Rebirth without self view is simply the continuation of suffering and the continuation of the chain of conditioned processes. It's not about the rebirth of a specific person or being or self or consciousness.

“Yes, friend,” he replied, and he went to the Blessed One, and after paying homage to him, sat down at one side. The Blessed One then asked him: “Sāti, is it true that the following pernicious view has arisen in you: ‘As I understand the Dhamma taught by the Blessed One, it is this same consciousness that runs and wanders through the round of rebirths, not another’?”

“Exactly so, venerable sir. As I understand the Dhamma taught by the Blessed One, it is this same consciousness that runs and wanders through the round of rebirths, not another.”

“What is that consciousness, Sāti?”

“Venerable sir, it is that which speaks and feels and experiences here and there the result of good and bad actions.”

“Misguided man, to whom have you ever known me to teach the Dhamma in that way? Misguided man, have I not stated in many ways consciousness to be dependently arisen, since without a condition there is no origination of consciousness? But you, misguided man, have misrepresented us by your wrong grasp and injured yourself and stored up much demerit; for this will lead to your harm and suffering for a long time.”
MN 38

“But, friend, when the Tathagata is not apprehended by you as real and actual here in this very life, is it fitting for you to declare: ‘As I understand the Dhamma taught by the Blessed One, a bhikkhu whose taints are destroyed is annihilated and perishes with the breakup of the body and does not exist after death’?”

“Formerly, friend Sāriputta, when I was ignorant, I did hold that pernicious view, but now that I have heard this Dhamma teaching of the Venerable Sāriputta I have abandoned that pernicious view and have made the breakthrough to the Dhamma.”

“If, friend Yamaka, they were to ask you: ‘Friend Yamaka, when a bhikkhu is an arahant, one whose taints are destroyed, what happens to him with the breakup of the body, after death?’—being asked thus, what would you answer?”

“If they were to ask me this, friend, I would answer thus: ‘Friends, form is impermanent; what is impermanent is suffering; what is suffering has ceased and passed away. Feeling … Perception … Volitional formations … Consciousness is impermanent; what is impermanent is suffering; what is suffering has ceased and passed away.’ Being asked thus, friend, I would answer in such a way.”
SN 22.85

Why now do you assume 'a being'?
Mara, have you grasped a view?
This is a heap of sheer constructions:
Here no being is found.

Just as, with an assemblage of parts,
The word 'chariot' is used,
So, when the aggregates are present,
There's the convention 'a being.'

It's only suffering that comes to be,
Suffering that stands and falls away.
Nothing but suffering comes to be,
Nothing but suffering ceases.
SN 5.10

"Then, Bāhiya, you should train yourself thus: In reference to the seen, there will be only the seen. In reference to the heard, only the heard. In reference to the sensed, only the sensed. In reference to the cognized, only the cognized. That is how you should train yourself. When for you there will be only the seen in reference to the seen, only the heard in reference to the heard, only the sensed in reference to the sensed, only the cognized in reference to the cognized, then, Bāhiya, there is no you in connection with that. When there is no you in connection with that, there is no you there. When there is no you there, you are neither here nor yonder nor between the two. This, just this, is the end of stress (suffering)."
Ud 1.10

I think this is excellent because it finally tells us what rebirth really is in Buddhism. It's not falsehood. It's not truth. It's just skillful means (upaya), a helpful tool. A middle way between falsehood and truth.

If we want to eradicate or remove something first we should know and aware about the thing that we wanted to eradicate. Similarly, Lord buddha taught us to remove or eradicate Sorrow, sadness, stress, whatever the things bring uncomfort bad feelings and keep us happy forever. For that we need to know what are the things that brings us unhappiness or sorrowfulness or mental and physical stress. In Buddhism we called them in One word "Dukkha".

Not only that he understood through his Omniscience wisdom that people have continuous travelling all over the 31 levels [4 Hells, 6 Heavens, Earth, 20 Brahma lokas] due to their own actions called "karma". This journey is called "Samsara". Also, he told us most of the time we were in hells due to bad actions and very rare that we spend our samsara journey as human or Deve or Brahma. This is the kind of Dukka we called "Jathi". Rebirth happening but we did not know of those feelings in this life. Because of that again and again we are doing bad karma which creates our next birth most probably in hell.

That is why he just wanted to stop traveling of this journey and be free forever.

In Buddhism what we experiencing now as "Dukka" little differ than the dukkha we know normally. This is the real explanation of Dukkha.

1. Birth is dukkha,
2. Aging is dukkha,
3. Death is dukkha;
4. Sorrow,
5. Lamentation,
6. Pain,
7. Grief,
8. Despair are dukkhas
9. Association with the unbeloved is dukkha;
10. Separation from the loved is dukkha
11. Not getting what is wanted is dukkha. In short, the five clinging-aggregates are dukkha." Buddha taught us to how can we overcome this agony and free for ever from this Dukkha.

For that he recommend us Four Noble truth with Eight fold Path. Four Noble Truths are:

1. The Noble Truth of Suffering
2. The Noble Truth of the Cause of Suffering
3. The Noble Truth of the Cessation of Suffering
4. The Noble Truth of the Way to the Cessation of Suffering

If we take an example: We can experience these truths, which lie at the heart of the Buddha’s teachings, through direct experience. They can be viewed as:

1. Diagnosis of an illness

2. Prognosis

3. Recovery

4. Medicine to cure the disease. The first 2 truths deal with the way things are; the last 2 point the way to freedom from suffering.

5. The Noble Truth of Suffering

Besides “suffering,” other translations of the Pali word dukkha include unsatisfactoriness, dis-ease, and instability. All these words point to the fact that no conditioned phenomenon can provide true (lasting) happiness in our lives. The first step in a spiritual life is to look very closely and honestly at our experience of life and see that there is suffering. We tend to overlook or ignore or just blindly react to the unpleasant, so it continually haunts us. Yet although physical suffering is a natural aspect of our lives, we can learn to transcend mental suffering.

2. The Noble Truth of the Cause of Suffering

Through a lack of understanding of how things truly exist, we create and recreate an independent self entity called “me.” The whole of our experience in life can be viewed through this sense of self. In consequence, various cravings govern our actions. Cravings arise for sense experiences, for “being” or “becoming” (e.g. rich, famous, loved, respected, immortal), and to avoid the unpleasant. These cravings are the root cause of suffering.

3. The Noble Truth of the Cessation of Suffering

The mind can be purified of all the mental defilements that cause suffering. Nibbana, the ultimate peace, has been compared to the extinction of a three-fold fire of lust, ill-will, and delusion. One who has realised cessation has great purity of heart, ocean-like compassion, and penetrating wisdom.

4. The Noble Truth of the Way to the Cessation of Suffering

The Way leading to cessation contains a thorough and profound training of body, speech, and mind. Traditionally it’s outlined as the Noble Eightfold Path:

1. Right Understanding;
2. Right Intention;
3. Right Speech;
4. Right Action;
5. Right Livelihood;
6. Right Effort;
7. Right Mindfulness; and
8. Right Concentration.

On the level of morality (sila), the Path entails restraint and care in speech, action, and livelihood.

The concentration (samadhi) level requires constant effort to abandon the unwholesome and develop the wholesome, to increase mindfulness and clear comprehension of the mind-body process, and to develop mental calm and stability.

The wisdom (panna) level entails the abandonment of thoughts of sensuality, ill will, and cruelty; ultimately it penetrates the true nature of phenomena to see impermanence, unsatisfactoriness, and impersonality.

When all 8 factors of the Path come together in harmony to the point of maturity, suffering is transcended. In summary, the Four Noble Truths can be thought of as that which is to be (1) comprehended, (2) abandoned, (3) realized, and (4) developed.

This is the clear precise way to Nibbana. All other context in Buddhism within this and explaining various ways to attain Nibbana. In other words for practising eight fold path Lord buddha taught us 40 activities we called them 4 meditation principles called :Sama Sathalis Karmasthana". All Suttra's were the one's Buddha preached different People, Deva[Gods], Brahma[Supreme Gods], Bhikku[Monks] and etc.to achieved Nibbana. You can refer these below links to learn more:

1. A path to Freedom
2. A theravada Library
3. The Great Higher Buddhism - Abhidhamma
4. The Forty Classic Meditation Objects May you be able to find the way to attain Nibbana!!! May Triple Gem Bless you!!!