The player should play what he wants to play, but I can't fault anyone encouraging him to play a cleric or other healer. Note: That's encourage (maybe even offering bribes), not bicker, whine, or brow-beat. If if the player decides to continue on with his other plans, that's the end of the story. The player gets to play what he wants to play (as long as it fits within the game world, etc).
I generally give my players enough rope to hang themselves. If the can't equitably figure out who plays what and there's overlap, that's fine. But they'll have to figure out their own way to cover their needs, whether it be by hiring an NPC cleric or buying a lot more potions, or having the bard pick up cure wounds spells. I won't force a player to play a cleric if they don't want to. Usually, at least one player is either flexible enough or doesn't have a set concept of his character in mind that he'll volunteer to be whatever character is lacking.
Browbeating and whining about things like this is a non-starter at the tables I DM.