Context is crucial here. There’re more meanings of “put sb down”, aside from that “criticize”.
As a sound bite taken out of context, it’s hard to type all of them.
You can “put somebody down as/for..” in a sense ( mostly pejorative one) of ranking him as a particular person with particular traits.
You can “put somebody down” in a sense that you leave him.( rare )
You can “ put somebody down” in a sense that you mop the floor with him ( both figuratively and physically )