No it's not. "Teach has gotten stronger after the timeskip, therefore he would now defeat Akainu" is a logical fallacy for more than one reason.
1. What proof is there that Teach's increase in strength places him higher than Akainu as opposed to him getting stronger, but not stronger enough to surpass Akainu?
2. What proof is there that Akainu hasn't also gotten stronger than he was in the past, and kept the gap between him and Blackbeard a constant?
Even if we go by feats BB after getting could possibly beat Akainu.
Possible? Yes. Likely? No. Teach's greatest feat was the same as the final Quake that Whitebeard hit Akainu with, and that Quake wasn't enough to even severely damage Akainu while hitting him at point-blank range.
What do u mean fallacy when it's clear that the timeskip was to produce more strength to the worst generation
Blackbeard and the Supernova do NOT have the same growth pattern. At the end of the timeskip, Teach was capable of injuring Sengoku. He had already been a pirate for a Yonko for decades and was well into his 40s. None of the Supernovas were even close to that kind of level. Just because they increased in strength tremendously doesn't mean that Teach has since he's already been building strength far before them, reaching the level of being able to injure Sengoku while they were stuck struggling against Pacifsta.
and BB who just got a new df has plenty off areas to grow on simply based of that
Teach was busting out the same power that Whitebeard was. The only thing he lacked due to his inexperience was the ability to control that raw power, but he already has as much power with the Quakes as Whitebeard did due to knowing about its abilities like the back of his hand before he got the fruit.
so that fact that BB even got a tad bit stronger puts him above Akainu who didn't get any stronger.
The fallacy returns, you don't know that Akainu didn't get stronger.