I just have watch a video and I saw this play, but I'm not convinced at all

UTG limps
SB (Hero) raises to 8 with AcKc
UTG calls

Flop: 2c 3c 4h
Pot: 18

Hero cbets 10
Villain calls

Turn: 9d
Pot: 38
Hero bets 12
Villain calls

We are playing vs a serious passive fish, who's playing 58/3.
The coach said in this spot, we can bet smaller vs this kind of player because there's no need to push any action, and with this bet we are trying to fold his weaker part of his range. The coach adds that he's is not folding much.

So my question is, why we are betting? Is it better to check and take our free card (assuming this passive fish is not betting)?