I'm taking a sociology class, and we just started talking about Marx. My professor asked us for examples of socialism, and quite a few people mentioned welfare.

I pushed back on this, saying that a redistribution of wealth isn't the same as "redistribution" (shared ownership) of productive means. My professor replied that socialism is a commitment to equality, which welfare provides.

Now, I wasn't sure exactly what to say next without denouncing capitalism. I'm also aware that my response could have been better. How would you respond to this?

EDIT: I'm not trying to convince my professor. I'm trying to present arguments that get my classmates thinking in hopes of radicalizing a few of them. One of the TA's actually pm'd me later saying that they agreed with me.