...because?

Time dilation is infinite at the even horizon, so anything that touches it, freezes for good.

The event horizon is not an object that can touch something, so why is that an objection to the idea of two event horizons crossing and uncrossing?

It's time itself that stops there. No matter what you want to move, you will have a problem moving it. It might be easier to understand that Democritean idea of space as literal nothingness is a bit old, in modern science space is field, i.e. solid matter (universe), particles move in it like sound for which steel is the most transparent medium, and nothingness is the most impenetrable, because there is no foothold there, we think it's empty because we can move freely in it.

Also most black holes have matter on the event horizon, because something fell on them. Maybe it can even touch, because this matter is frozen slightly above even horizon.

Time has also stopped for photons, which does nothing to stop them from moving from place to place.

I don't see a way to read your comment that allows for the possibility that a black hole might move, which is something they do.

I'm riiiiiiight on the edge of concluding that you are a poet and the only thing you know about the words is the way they sound. Is there more to it than that?

Technically time is exponentially dilated, this introduces large relativity of synchronism: the same thing takes different time in different reference frames. You aren't completely wrong to say black holes will fly through each other, but this doesn't take the same time in all reference frames. For a distant observer it takes infinite time after their event horizons touch, and Hawking radiation evaporates everything before that.

How black holes can move is an interesting question, but as you can see, in reality there are no infinities, since stuff slows down before that. Maybe infinities could exist for an observer inside black hole, but an observer outside of black hole sees only large slow down.

Infinities are typically indications of where a theory breaks down, not of something real.

Infinity there isn't abrupt, but steadily grows. Anything that approaches just does it slower and slower, and remains always finite, only exponential.