Is OTHER wrong in the post ? POST : Hello r/AITA, this is a throwaway since I do not want to be identified.

Today, I got annoyed like again because my friend said that his family was so poor that he ate only Tuna as meat for 6 years straight. This was such a clear exaggeration. I responded "I have some doubts about that" and he doubled down on his response. Not only this, he would say that he has a depression whenever he is just slightly sad (he is perfectly social and happy for like 80% of the time). He also always implies that he is 'so poor' when he is clearly much better off than many others in the friend group. I often get annoyed and try to tell him that he should not exaggerate things as such but when he replies that he is not, I am not sure how to respond further. Now, I disregard many things he says, although he does claim what he says is true. Am I the Asshole for this behavior?