It just depends on your agreement with the company. There's no reason that by default they own everything you do, beyond the fact that business has normalized it (and many other practices with the magic words 'it's just business').

Umm, but your employer is also taking time from you so you definitely can say that in reverse.

In fact, your employer is taking your a fragment of your life, and human life is worth more than currency, so actually, it's really quite inappropriate if your employer was found accidentally using ideas that you had while you were in the shower at home when they weren't paying you. (internet you-can't-hear-my-voice disclaimer: this is obviously hyperbole meant to really drive home the point.)

I'm generally a fan of market-based methods of structuring economic activity, but this sort of implicit assertion that the owner of capital is just obviously more important than the owner of labor really puts the "ism" is Capitalism.

Labor is a market, and markets are determined by both the players and the rules under which the players compete. Companies use the force of law to coerce laborers (see: every other post in this tread where supposedly free people worry about being sued). It's completely fair game for labor-force participants to turn around are use that same force to coerce employers.