Spoken like a true economist talking from the ivory tower.

Just because average inflation is the same, doesn't mean every product's inflation is the same.

You will see much larger inflation in goods everyone needs, especially low income housing, and maybe some deflation in luxury goods.

On average theres maybe no inflation, but you haven't actually helped the poor. Well done.

Your argument rests on the assumption that poor people consume a set of goods completely distinct from middle income and wealthy people. If the price of a loaf of bread increases by 200% in an attempt to take advantage of increased purchasing power, why would the wealthier consumers accept this, if their income had not increased? Competition would put an end to rent seeking behaviour.

And on the subject of low income housing, it's often highly regulated, and can't be hiked arbitrarily.

If I've understood correctly, your argument is that the inflation in the basket of goods consumed by low income people exactly cancels out the increased purchasing power, I'm not sure you can argue that's definitely the case.

While my argument surely had some simplification, it holds approximately.

Whereas for your argument, I’m not sure how you come to the conclusion that inflation will cancel out all benefits. There is no reason to assume that.

Basic goods demand is fairly stable. Poor people will always need to pay for food, shelter, etc. Just with basic income, they won’t have to worry about how they’re going to scrape together the money next month for the rest of their lives. These inflation concerns also assume zero elasticity on the supply side, which seems odd since there is no monopoly situation on any basic good, with the exception of housing in specific areas. Fortunately, the ability to move places strongly increases with a guaranteed income too.