1. Let's say someone wants your HN username, andrewhillman. You've been inactive for a few months. What do we do with your old posts and comments? Deleting all the data for inactive users seems like an awful approach. If we keep the data, you lost your username, so what's displayed beside your comments? Do we just replace your username with the word, inactive? What about your profile? If I come across your old comments, enjoy them, and want to see your profile, I obviously can't go to https://news.ycombinator.com/user?id=andrewhillman any more, so where is your profile moved to?
2. People expect their identity to remain consistent. What happens if you take a season off HN since you're busy at school? Meanwhile, you have links to https://news.ycombinator.com/user?id=andrewhillman on your linkedin profile, or your website, or maybe you have business cards or flyers printed with that URL. Uh oh, you come back to HN, and that profile now belongs to someone else. All those great contacts you recently made, and gave business cards to, they're browsing the HN profile for someone else, believing their opinions are your own.
Ok, now printing your HN profile URL is unlikely, but what about your Twitter? Or Facebook? Or Gmail? This could be a disaster if you have hundreds of links to your Twitter account in blog posts and comments around the internet, then you decide to abandon Twitter. Someone else takes the account name, and has a less than stellar reputation. Lots of communities will not allow you to edit posts past a certain date, so you're out of luck, and all your old data is asking people to follow you on Twitter, andrewhillman. Meanwhile, that account now belongs to someone posting NSFW images.
As someone else said, it depends on the service. In some situations you might be able to allow non-unique usernames, so you wouldn't have this problem to begin with. Another solution could be unique usernames, but linking profiles to IDs, instead of specific names. That way old links still function properly and don't change with usernames. Of course, it makes for longer and ugly URLs.
120 days seems incredibly short though. I'd say 1 year minimum before declaring an account inactive.