These are all just specific cases where one can reasonably make arguments to say "yes" or "no", but have a different opinion for other specific cases.
For your first 3 examples (romantic, friendship, student/mentor), I of course say sure, either party is free to leave whenever they want.
The difference here is an economic one. It's near impossible to make sensible legislation around feelings (though some lawmakers certainly seem to try). While the ending of a romantic relationship may have a huge negative psychological impact on me, it doesn't affect my ability to live on in economic terms. A landlord kicking me out of my apartment can directly affect my livelihood, and the government is trying to protect me there. I think it's also uncommon for that to hurt the landlord (especially in the non-rent-controlled case), so there's an imbalance of pain. In the relationship case, leaving causes me pain, but staying causes the other person pain. Legislating whose pain is worse or less justifiable is, I hope we'd agree, a mess.
The firing topic is interesting, though, because even the law disagrees in different parts of the world. In Europe, for example, many countries have laws that are very employee-centric, and make it very difficult for firms to fire people. I personally don't agree with the extent that they've gone over there, but I can at least appreciate that people in other areas value employee security over employer mobility and lack of overhead. Even different states in the US have different laws that make it easier or harder to fire people, and define different obligations on the employer when they want to fire someone.
All relationships are a two-way street, and for a fair trade, both parties have to agree, voluntarily.
I'd like to agree to that in principle, but that just isn't true. There are plenty of laws on the books that can give one side more rights to make, not make, continue, or terminate an agreement. For example, a landlord may wish to discriminate against people with certain physical disabilities, because otherwise he'll have to spend money to install accessibility features in his building, but the law says... nope, can't do that.
A landlord may also wish to discriminate against an existing tenant who isn't able to fulfill the landlord's newest vision of his property's profit-making abilities, but there are a bunch of laws that also say... nope, can't do that. I happen to agree with a lot of them, or at least the intent behind them.
Our entire legal system is based on the idea that, on an individual level, both parties don't have to agree... only some representatives pulled from the majority do... sorta. There are lots of laws on the books that I never agreed to, and yet I'm bound to follow them just the same.
But all that is fine, I think. Many laws -- renting-related laws in particular -- are designed to weaken inherent power imbalances. The landlord naturally has more power in society than the single mother who is holding down two jobs. The law tries -- often imperfectly -- to protect the mom from people who would ignore her interests and take advantage of her.