I'm a little surprised to see the Bishop article call it a light trasher.
It trashes cards, so it's a trasher...
Well, fair enough, but the article lumps it in with cards like Salvager, Remodel, and Island, which have the effect of improving your deck without improving your opponent's deck, so that it's a net improvement for you. In the early game, Bishop plays are not a net improvement to your deck, because your opponent benefits equally.
POTENTIALLY benefits equally. But there's some cost for them doing that. Which may or may not be worth it.
If you and your opponent trash the same card, then the cost to them is the same as the cost to you. (Assuming that you're following roughly similar strategies. Obviously this doesn't apply if they are doing Gardens, etc.)
Consider for example a symmetric copper case:
You draw Bishop, 4x Copper. Your opponent draws Silver, 4x Copper. If you trash a copper with your Bishop and your opponent responds by trashing a copper too, then you have $4 to spend, your opponent has $5 to spend, and you got a VP token to compensate. If Bishop didn't have a trash effect, you'd have $5 to spend and your opponent would have $6 to spend. So you both lost $1 in the current hand and have the benefit of one fewer copper in deck. (Your opponent might choose to not trash a copper in order to buy a gold. But this is an option--they'd only choose to do it if it's better than being equal!)
A symmetric estate example:
You draw Bishop, 3x Copper, Estate. Your opponent draws Silver, 3x Copper, Estate. If you trash an estate with your Bishop and your opponent responds by trashing an estate too, then you have $4 to spend, your opponent has $5 to spend, and you got 2 VP tokens. Spending amounts this turn are unaffected by the trashing, and you both trimmed your deck equally (an estate less for both).
Asymmetric cases are where the Bishop player can get an edge, but in the early game I think it should balance out. (If one player trashes a copper and the other an estate, it's better for the estate-trashing player, no matter who played the Bishop.)