Building a switch is (relatively) easy. Building a switch that can offer acceptable performance in a box with enough ports on it to be useful is harder.
It's not immediately obvious what advantage you'd gain by doing that anyway, since you can just buy a white box switch and run your own software on it.
There are chips out there already, aren't there? I think the Turing Pi board has a switch built into it (and an ethernet chip per slot, which is maybe not so good)
Yes, those are what you'd expect to find in the white box systems I mentioned, and most branded off-the-shelf switch products for that matter. But if that's what you need, I'm not sure what the advantage is to building your own hardware instead of buying one of the ready-made options. It seems like you'd need to have quite eccentric requirements before it was worth seriously considering designing and building a whole system of your own instead.
It's not immediately obvious what advantage you'd gain by doing that anyway, since you can just buy a white box switch and run your own software on it.