I am so confused by, for example, "People love their life or lives."

For sentence one:

Look at it like this, 'He loves his life' and 'She loves her life' are obviously correct.

Now, when we we say 'People love their _ .', we can mean two things:

1. They love their own lives (separate lives) .
2. They love the life that they are having together or share.

Example:

• 'Software developers love their life' would mean that software developers love the life of software development.
• 'Software developers love their lives' would mean that the group of software developers you are talking about, love their own individual lives.

Under no circumstances would I permit a singular object in either sentence 2 or sentence 3. In both cases, the subjects of the sentence are called "plural generics," the grammatical term for the use of the plural noun to create a generic class. [See this explanation of plural generics][1]. As with any other subject and possessive object, the generic plural must agree with the number of the subject when a possessive is used. For example "Everyone take his seat," is correct, but *"Everyone take their seat," is NOT correct, even though people often say it. "Everybody take their seats," is also fine, because 'everybody' is plural, while 'everyone' in this context is singular. In fact, the phrase "everyone take their seat" could only be correct if you were instructing a group of people ("everyone") to take the seat of another group ("their"--that other group over there's--seat). Similarly, the same rules apply for generic plurals.

You can read more about generic plurals, and a special case called the 'generic they' here.