Why do you have sadness in the first Jhana?

It's not clear why asking, since the answer is contained in the question already. There are two kinds of sadness, of one is that of a housholder and the other of one having gone forth.

There is a "cutting off" which is compiled with wisdom and leads as already stated to path elements.

But since you see no reason to leave home and keep on holding a stand, how could you ever experience the meaning of giving and let go? Only one how let go knows what let go means. There is no possibility to explain. Never turn around to manage it.

(note that this is not given for trade, stacks, exchanges and entertainments which will naturally cause you unskilfull sadness but as a tiny door out of this wheel)

Sadness exists in the first jhana because it has not been eradicated yet. Sustained and focused thinking, thought in general, and cognitive processes still have free reign in the first jhana. Only in the second jhana are the ruminating thoughts reigned in.

"There is the case where an individual, withdrawn from sensuality, withdrawn from unskillful qualities, enters & remains in the first jhana: rapture & pleasure born from withdrawal, accompanied by directed thought & evaluation. He savors that, longs for that, finds satisfaction through that. Staying there — fixed on that, dwelling there often, not falling away from that — then when he dies he reappears in conjunction with the devas of Brahma's retinue. The devas of Brahma's retinue, monks, have a life-span of an eon. A run-of-the-mill person having stayed there, having used up all the life-span of those devas, goes to hell, to the animal womb, to the state of the hungry shades. But a disciple of the Blessed One, having stayed there, having used up all the life-span of those devas, is unbound right in that state of being. This, monks, is the difference, this the distinction, this the distinguishing factor, between an educated disciple of the noble ones and an uneducated run-of-the-mill person, when there is a destination, a reappearing.

"Again, there is the case where an individual, with the stilling of directed thoughts & evaluations, enters & remains in the second jhana: rapture & pleasure born of composure, unification of awareness free from directed thought & evaluation — internal assurance. He savors that, longs for that, finds satisfaction through that. Staying there — fixed on that, dwelling there often, not falling away from that — then when he dies he reappears in conjunction with the Abhassara[1] devas.[2] The Abhassara devas, monks, have a life-span of two eons. A run-of-the-mill person having stayed there, having used up all the life-span of those devas, goes to hell, to the animal womb, to the state of the hungry shades. But a disciple of the Blessed One, having stayed there, having used up all the life-span of those devas, is unbound right in that state of being. This, monks, is the difference, this the distinction, this the distinguishing factor, between an educated disciple of the noble ones and an uneducated run-of-the-mill person, when there is a destination, a reappearing."

-- from AN 4.123 PTS: A ii 126
Jhana Sutta: Mental Absorption

You are quoting sn48.40.

In this sutta, the following five faculties are transcended as one enters various jhanas:

1. pain: first jhana
2. sadness: second jhana
3. pleasure: third jhana
4. happiness: fourth jhana
5. equanimity: "ninth jhana"

Pain is coarser than sadness, for both householders and Noble Ones.

For a householder, someone sad over the death of a loved one might not notice ongoing pain from illness or injury--the personal sadness exceeds the personal pain.

For a mendicant, as personal bodily aches and pains recede with first jhana, one becomes more aware of the immense suffering of others and a sadness arises out of that awareness. Or an older mendicant might feel sadness arise from realizing that Nibbana might be personally unreachable in this very life.

One can also personally experience the relative coarseness of pain vs. sadness without jhana in regular meditation. It's actually quite interesting to meditate when one is in pain and/or suffering. They both attenuate, but pain attenuates first.

Lastly, just because sadness or pain disappears does not mean one has attained one the above jhanas--there are other conditions. There are also different degrees of pain and sadness.

The first jhana is where we sit and deliberately think about our luck of encountering true Dharma and our circumstantial advantages over regular people, in order to transform our insatisfaction with personal life into joy. (e.g. Instead of thinking that having no money, no friends etc. is horrible, we sit and think that we are lucky to be uninvolved in Samsaric activities etc.) We also think about typical problems of the worldly people in order to transform our hatred of the world into compassion.

This deliberately contrived change of perspective brings understanding that we are much luckier than regular people, and that regular life is actually pretty bad. This brings joy about ourselves, and at the same time it brings sadness about the regular world and about life in general.

This sadness or grudge towards life is domanassa described in this sutta.

Then on the second jhana, you do not think - not in the sense of forcing your thoughts to stop, but in the sense of not using the comparisons anymore. You just sit there and cultivate an overall feeling of no conflict, feeling of peace and unification, feeling of rightness, feeling of confidence, of being sure, feeling of being strong. This is a much more refined meditation at this point, but Buddha said, you can't just jump to it, first you must learn to overcome coarse craving/aversion, and generate coarse joy using your thinking, and once you get good at that, then you can practice the second jhana.

On the second jhana you do not use coarse thinking, you do not polarize Everything into "awesome I" and "sad world". Because you do not polarize, sadness is not generated.

This is an interesting question, because the first jhana explicitly involves seclusion from the five hindrances, one of which relates to domanassa (translated in your quotation as "sadness"). According to the abhidhamma, domanassa can only arise in anger-based minds, which one might think would be totally absent in the first jhana. The commentary to SN 48.40 blames vitakka and vicaara explicitly for the potential arising of domanassa:

nānāvajjaneyeva ca dutiyajjhānupacāre pahīnassa domanassindriyassa yasmā etaṃ vitakkavicārapaccayepi kāyakilamathe cittupaghāte ca sati uppajjati, vitakkavicārābhāve neva uppajjati.

My Pali is rusty, but this passage basically means that the bodily distress and mental harm which would arise based on vitakka and vicaara do not arise with the non-existence of vitakka and vicaara.

This gives some insight into the nature of vitakka and vicaara as per the texts; they allow for some instability by which the mind still engages in perceptions leading to domanassa, even though the mind is otherwise fixed and focused on a single object (ekaggata).