Is it illegal to give away beer to someone over 21 for free?

Only in my household. I charge all of my friends which is probably the reason I'm watching baseball alone this afternoon. All kidding aside, I don't believe you could charge him without a liquor license.

It is not illegal to give someone a beer who is lawfully entitled to have it.

Alcohol law is kind of arcane and complex at times. If you're a private party on private property, I'm sure there's no issue. If you're a private party on public (or quasi-public) property, it would probably depend on the local ordinances. If you're a business and are giving away beer, there may well be an ABC agent knocking on your door sooner or later. Local police are unlikely to care, even if it is not truly kosher. ABC, though, is notoriously stringent. If you are talking about a business practice, I would encourage you to contact ABC directly for guidance and/or an attorney who specializes in liquor law compliance.

If the free beer is for an attorney then it is legal (and encouraged).

No it is not illegal.