Because his wand was snapped in two when he was expelled from Hogwarts in his third year, and his broken wand is now concealed inside his flowery pink umbrella.
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Rubeus Hagrid.
Axle grease.
Hagrid is not supposed to use magic because he got expelled from Hogwarts and had his wand broken in half. It is also the first time that somebody has stuck up for Harry when he is being bullied by the Dursley's which shows the change about to happen in his life and helps his friendship with Hagrid.
As far as I can remember, the books don't really analyze this question. However, there are a few points that may have helped Harry believing Hagrid:* Hagrid's personality may have helped. * Hagrid himself is "unbelievable", being a half-giant. * Hagrid did some magic himself. * The letter from Hogwarts. * Uncle Vernon's reaction to Hagrid wanting to tell Harry the truth. * Harry's previous experiences with magic (he had accidentally done magic, now and then).
Hagrid decided to buy Harry's animal and gift it to him as a birthday present. Hagrid is allergic to cats as they make him sneeze and Toads were old fashioned, students would have laughed at and made fun of Harry and Hagrid didn't want that