Give is dać or dawać.

Podać means that the subject is taking the direct object in order to bring it closer to the indirect object and then give it to them, because the indirect object couldn't reach the direct object themself. So, in plain English: passing.

Of course sometimes it's acceptable to use the verb give to refer to the above act, similarly, it's also sometimes acceptable to use the verb dać, but Duolingo wants people to be precise and distinguish passing from ordinary giving.

"Daj mi moją kurtkę." – Give me my jacket. is perfectly fine, but suggests that the listener is somehow holding to the speaker's jacket for quite a while before being asked.

Isn't it always? I personally think it should be...