The idea is that transit has benefits beyond what it gives to the riders. If a bus takes 20 cars off the street that's a huge boon to the other cars.
In Ithaca, for instance, Cornell doesn't have a lot of space for parking, if you do get a parking space it is probably far enough away that you'll ride the bus in anyway. Employees get a free bus pass and even though it means I have to fit my schedule to the bus, it drops me off right by the door of a building that's connected to my building so it's as convenient as can be.
The problem with every one of these posts is the same: IS it compensated by X? No. Why not? Because X is not happening, and the city is certainly not paying for it with the extra income.
You talk about a free bus pass, but you might as well talk about free use of a Star Trek transporter. I would argue that'd be more honest, because if you talk about a nonexistent transporter technology at least it's clear that it's not happening. Also: this is New York. The bus service would need to be improved as well. That too is not happening. Nobody would be complaining in the first place if there was cheap (you even say "free"), fast and good public transport. There isn't.
I don’t think the person you replied to said that congestion pricing is bad.
Between the lines you read that congestion pricing makes cars more expensive, and that would/should be compensated by making public transport cheaper.
And my remark to that is that the state ISN'T making public transport cheaper (in fact the opposite), on top of that the state is disregarding the other problems with public transport, like safety, maintenance and coverage. And further savings on public transport are being implemented in New York. So, to make it very general, this congestion charge is punitive. It's making the situation better for some (people who pay the congestion charge) by making the situation worse for everyone else. It's making the situation better for rich people, who have a far easier time living more comfortably outside of New York, who can now buy easy access to New York far cheaper.
How is public transport costing too much a problem caused by congestion charges? It may be true, but I don’t think causality works like that.
Obviously, there are more causes than just this, including sabotage because the US dislikes public transit in general, but contracting is a massive cost that kills in-house talent and wastes money on every project. And of course I don't expect them to do zero contracting either - I don't expect them to start manufacturing their own trains, for example. Right now, however, the balance leans far too much on the side of "too much contracting".