If a 200 pounds man gains an additional 50 pounds of fat he will be stronger than before. Why is that? How does fat contribute to lifting stuff?
Fat does not naturally make you stronger by just existing. It's inactive. It just sits there. You can't control it.
I think the misconception that fat inherently makes you stronger is brought on by two observations.
First, people don't just gain fat. They gain muscle as well. Even untrained people will gain muscle in addition to fat. People with more muscle are just going to be stronger regardless.
So in your scenario, a person going from 200 to 250 lbs. is not going to gain 50 lbs. of fat. They might gain 40 lbs. of fat and 10 lbs. of muscle. If they trained really hard, then they would gain maybe even more muscle and less fat. They will end up looking "fat" because their frame grew bigger and you can't see any of the definition because of all the fat gain. In reality they have a considerable amount more muscle.
Second, there may be specific sports in which being excessively heavy is an advantage. You see this in sports like in Strongman, American football, wrestling, or basically any sport where someone or something is pushing up against you.
In the case of wrestling or football (specifically linemen), they have two jobs (very oversimplified so please don't get mad). The first, primary job is to push the person they're facing and move them to somewhere else. That takes brute strength. The second is to not be pushed because their opponent is trying to move them. It's considerably harder to push someone who is 400 lbs. than someone who is 200 lbs. So there would be an advantage to being bigger.
Likewise, in Strongman, there are specific events in which the weights are imbalanced. For example, in the yoke, the person has to walk while carrying a significant amount of weight hanging from their back. That weight is going to swing and move around which in turn is going to push the lifter around with it. A lighter person is going to exhaust a significant amount of energy trying to maintain balance while walking whereas a heavier person can use their weight to counteract the force. So it might give the illusion that the heavier person is stronger, but in reality they're doing less overall work (this is of course assuming that these two people have the same amount of muscle, training, etc).