Gabi, he writes that it is his Minhag. He mentions that some have the Minhag of celebrating the Bris day, but it is not his Minhag. He does have a Teffila for that day, though.
The reference of Noach Lo Shelo Haya Nivra is more about what would have been better. To be upset about being created goes against every Teffila of Hodaa. We always thank Hashem for life. The Maharal writes that although it would be easier not to be created we bend our will to the will of Hashem. That is why the Gemara says that we should thank our grandparents, who if not for their Cheit we would not have been created.
Think of it this way. It is definitely easier to remain a child but the fact is you grow up, and celebrate it, too. (I’m not just referring to the Seuda of Bar Mitzva. I’m talking about any human that celebrates growing up.)
Some feel that pointing out the older age can cause Ayin Hara, while the Ben Ish Chai says that it is a good Siman. Bilvad Sheyichaven Libo Lashomayim.