I don't think wanting to occasionally do something with your partner is unreasonable. The issue isn't really whether your partner is a homebody. It's whether there is room in the relationship for what matters to you as well.

You shouldn't expect somebody to completely change their personality, but neither should accepting somebody as they are mean that one person's preferences dictate the entire relationship.

I'd have a conversation about how this makes you feel rather than about how often they leave the house. Saying ‘you never want to do anything’ will probably produce a defence. Saying ‘I'm starting to feel lonely because we don't seem to experience much together’ explains the actual problem.

Then make the compromise realistic. You aren't asking for three nights out every week. Perhaps agree on one proper day or evening together every few weeks and take turns deciding what you do.

What matters most is their response. They don't have to suddenly enjoy going out, but they should care that something is leaving you unhappy. A relationship needs some movement from both sides.