There's a lot to like about functional programming, and I do, but one thing annoys me: its name. "Functional" has two senses, both of which are important concepts, and which have nothing to do with each other.
One sense is using functions as first-class values. This is such a powerful feature that it's surprising it's not yet universal. You might unambiguously call it "high-order programming", but hardly anyone does, because "high-order" sounds so affected.
The other sense is programming by constructing new values instead of modifying existing ones. This is not so much a feature (although it does depend on automatic memory management) as a failure to abuse one, so it's odd that it needs mentioning at all. State is a powerful, versatile tool, but you don't have to use it for everything! (Well, implementationally you do have to use it for everything, which is how the habit got started, but it doesn't have to be exposed.)
Both senses are important, and each one is valuable independently of the other. It's perfectly reasonable to wrangle state with combinators, or to avoid mutation in a first-order language. But in practice they're found in the same languages, and called by the same name, so it's easy to get them confused.
Here's a discussion which exhibits this confusion, starting with an extra bonus: some people appear to think "functional" implies static typing! Fortunately this is not widespread. I think it's just a result of sloppy ML advocacy; I haven't seen anyone defend it after the mistake was pointed out.