It's hard to do irreparable damage to the steel of a knife. It's just an inert lump of metal. But you could fuck up the handle. Theoretically, the detergent could dull your edge. If you don't isolate your knife and it rattles around, that'll definitely dull it. Mostly: it should only take a couple seconds to clean off your knife in the sink.

The steel used to make the knives is not always stainless, so it can stain or rust. Even stainless is really just stain resistant.

Dishwasher detergent is caustic and corrosive to steel, so over time it can pit the metal and dull the finish. Handles will swell and become loose or deteriorate, either because of wood repeatedly being waterlogged and dried or just from the heat cycling. A loose handle can be unsanitary, unsightly, dangerous, or all three.

You'll often read that knives in the dishwasher will bang around and that will damage the edge. And that it's more likely you will hurt yourself pulling a knife out of the dishwasher vs. cleaning them properly.

Phosphoric acid detergents will pit your blade. If the knife is not a stainless steel, the wash and dry cycle will cause accelerated rusting. In wooden-handled knives with a rat tail tang construction, you can start destroying the handle from the inside out due to gaps in the construction allowing water seepage and degradation. In non-stainless knives, that same construction becomes the point where rust tends to build up.

Then you also have the action of the dishwasher water jets bouncing the knife around, dulling and destroying the edge.

Only the shittiest cheapest plastic-handled knives I own touch the dishwasher. Everything else gets cleaned and wiped by hand and put straight to the knife block or its respective scabbard.