Why is sulfuric acid considered a Bronsted acid?

Because it is a proton donor in aqueous solution.

The first protonation:

##H_2SO_4(aq) + H_2O(l) rarr HSO_4^(-) + H_3O^+##

This reaction goes to completion in water.

However, the conjugate base of sulfuric acid, bisulfate anion, is itself a reasonably strong Bronsted acid:

##HSO_4^(-) + H_2O rarr SO_4^(2-) + H_3O^+##

Overall, ##H_2SO_4(aq) + 2H_2O(l) rarr 2H_3O^(+) + SO_4^(2-)##

As in any chemical reaction, both MASS and CHARGE are conserved.

PS I once asked a Scandinavian, who was an excellent linguist, what was the difference in pronunciation between ##"Bronsted"##, and ##"Brønsted"##. Given that he knew that I am a very poor linguist, he just laughed and said not to bother.