How can I explain soullessness to other one?

Both claims "the soul exists" and "the soul does not exist" are correct, as long as they are not coming from ignorance.

According to the Buddha ignorance is having the view "self exists".

Thus it follows ...

• If you claim "the soul does not exist", your claim is correct as long as it is not coming from the view "self exists".

• If your friend claims "the soul exists", her claim is correct as long as it is not coming from the view "self exists".

Now listen carefully as I will speak ...

When a being holds the view "the soul exists", that being, at the time of holding onto this view, must also hold the view "self exists".

Why is that so?

In order for the soul to exist, there must be a cognition of existence of the soul. With cognition of existence of the soul, even if the soul truly does not exist, the soul exists.

Thus, for existence of the soul to be cognized, a cognition of existence of a soul is needed, and what else is a cognition of existence of a soul then a kind of self itself?

Thus, in order for the soul to exist, there must be a kind of self with a cognition of existence of a soul.

That is why a being who holds the view "the soul exists", also holds the view "self exists".

When a being holds the view "the soul does not exist", that being, at the time of holding onto this view, must also hold the view "self exist".

Why is that so?

In order for the soul to not exist, a cognition of existence must not exist. Without cognition of existence, even if something/anything truly exists, nothing exists.

Thus, for existence not to be cognized, a cognition of existence must not exist, and what else is a non existent cognition of existence then non existence of self itself?

Thus, in order for the soul not to exist, there must be non existence of a self.

That is why a being who holds the view "the soul does not exists", also holds the view "self does not exist".

When a being holds the view "self does not exist", that being, at the time of holding onto this view, must also hold the view "self exists".

Why is that so?

In order for the self to not exist, there must be a cognition of non existence of the self.

Thus, for non existence of the self to be cognized, a cognition of non existence of the self is needed, and what else is a cognition of non existence of a self then a kind of self itself?

Thus, in order for the self not to exist, there must be a kind of self with a cognition of non existence of the self.

That is why a being who holds the view "self does not exist", also holds the view "self exists".

That is why a being who holds the view "the soul does not exist", also holds the view "self exists".

...

This being said, having a view "the soul exists" or having a view "the soul does not exist", can both come from the ignorant view "self exists" described above, which is, according to Buddha, ignorance. Which is, according to Buddha, the cause of rebirths and all the mass of suffering.

That being said, all views, including the views "the soul exists" and "the soul does not exist", must be abandoned as they do not lead to the cessation of suffering. In the same way as you would let a bird you caught with your hand, thirsty for freedom, out of your hand, all views must be abandoned.

http://www.accesstoinsight.org/tipitaka/sn/sn44/sn44.006.than.html

Speculating about these views does not lead to their abandonment.

Meditating and reaching complete cessation, coupled with insight, leads to their abandonment.

Only then, once these views have been abandoned and ignorance removed in its entirety, one can, out of compassion for other beings, expound the truth and use such terms as "the soul exists" and/or "the soul does not exist" as a vehicle that can be used by beings to achieve liberation.

I have practiced mindfulness meditation and studied the Theravadin Abhidharma for more than 50 years. I can tell you with absolute certainty that Buddhist psychology cannot be understood without relevant experiences in advanced states of mindfulness meditation. Buddhist literature is not able to deal with the sophisticated definitions and arguments offered modern philosophy and psychology. There is indeed a mental organism that reincarnates from lifetime to lifetime. The Buddhist description of this organism is incomplete. I suggest that you and many Buddhist monks do not know and do need to know what this organism looks like or how it actually behaves. Such knowledge is irrelevant to achieving Enlightenment. If you really want to more about what I have discovered in meditation, you can read my books. Both you and your friend have no way of knowing what the concept of no-self or soul really means. My name is Ronald Cowen.

Ask her to point out anything that qualifies as a soul. Then she will tell you something that comes under the 5 aggregates. Then you can teach her the Anatta-lakkhana Sutta

Both soul exists and soul does not exist are extreme view:

Ananda, if I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, that would be conforming with those brahmans & contemplatives who are exponents of eternalism [the view that there is an eternal, unchanging soul]. If I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, that would be conforming with those brahmans & contemplatives who are exponents of annihilationism [the view that death is the annihilation of consciousness]. If I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, would that be in keeping with the arising of knowledge that all phenomena are not-self?

Ananda Sutta

Simply there is nothing worthy of identifying as self, because you are not in control, whatever you identify as self are not entirely pleasant.