500 Rummy
The aim of the game is not to go out first. It is to score as many points as possible.
Melding cards will reduce your points loss if your opponent goes out. But it can also give you opponent a way to meld cards they have in their hand. Time when you meld carefully.
Melding runs offers a greater chance of your opponent being able to meld a card they have in their hand than melding a set.
Holding cards which offer the possibility of meding as both a run or as a set gives you a greater chance of drawing a useful card.
The more cards you have in your hand, the greater the chance that drawn cards will complete a set and score points. Balancing the risk of having a large hand with the chance of your opponent going out is the key to the game.
Discarding a card which is useful to you may not be a bad move if it is useless to your opponent.