I’m not a competitive player, but for me castling is not something you should work toward. I mean, while I move those >3 pieces (king’s pawn, king’s bishop, king’s knight OR queen’s pawn, queen’s bishop, queen’s rook, then queen twice = 5 moves) the enemy is attacking. Also, the pawn moves are clumsy if you move DIRECTLY into castling - remember, the defenders of the King are the diagonal ones. It’s very easy to see a potential attack from dead ahead, but harder to see the diagonals.
I did this a few times before deciding that castling should ONLY be incorporated into another set of preparations for attack.
So, in the course of my first ten moves, I might move those things out and THEN castle.
Another reason why castling isn’t too good is that it’s constrictive - it’s easy to attack the rook or defending pawn with a backup to prevent counterattack with the King - usually a checkmate.
Oops! That should be 10…P-N3 and mate in two.
Generally speaking, castling is good. Among the top players, castling is done by both sides around 95%, I would guess, but the question is when. You don’t want to castle too early necessarily, although there are plenty of standard openings that castling is done within the first six moves. If the other guy has castled kingside, then you would be safe to do likewise, unless there are other pressing exigencies. It depends upon your style, actually. If one side has castled kingside, it is generally safe to do likewise, but do you just want to play it safe? If you wait, attack, and probably castle queenside, you will run into risks, but if you are an attacking player, this may be the way you wish to play it. If you are not an attacking player, then you may want to castle kingside also.
For a beginning player, your brother’s explaination of castling is more than adequate, alice_in_wonderland. One just has to bear in mind that, in the end, castling is just a move (albeit a somewhat special move) and needs to be weighed against other reasonable moves. You always want to get all your pieces into play, keep your king safe, and get something going, but you’re only allowed to play one move at a time, after all. Hence the reason that castling “as soon as possible” is not always the best approach.
As a counter-example, I generally castle relatively late in games (and on rare occasions, not at all). That’s usually because I tend towards a rather risky style of play. While I want a safe king and a more active rook like any other player, I’m sometimes too busy making threats against my opponent’s position or, more likely, defending weaknesses in my own position to spend a move to castle. Also, I sometimes play into situations that involve both players going for an all-out-attack against the opponent’s king. In those situations, I prefer to delaying castling so as to keep my opponent guessing as to where my king will finally be deployed. But these are position-specific examples of why it might not be ideal to castle early, and are typically the exception, not the norm.