Why, in America, do you have to enrol to vote for a particular party?

I don't know. I hate our system. I also hate we go by electoral votes, not individual.

It is due to the primaries. Each party has a primary to decide who will be on the ballet for each party in the general election. You can only vote in the Democratic primary if you are a democrat, and you can only vote in the republican primary if you are a republican, the same rule applies for independents. When the general election comes, then your ballot will show everyone. Keeps one side from goofing up the other by putting weak candidates on the ballot.

You don't have to. Some people choose to. I have never affilliated myself to any party, I vote as I see fit.

Coloco is right. I'm not really fond of the system, but since people aren't trustworthy, that's what we're stuck with. Since I am registered independent, I can't vote in primaries.

coloco is partly correct
All states don't require party voting in the primary.

For example, in Indiana where I live, the primary vote requires me to declare a party, then I am only allowed to vote for people in that party. The choice to vote on the Democrat or Republican ballot has nothing to do with anyone's party affiliation. (in Indiana).

In Michigan, where I used to live, the primary is open. Anyone can vote on anyone in the primary.

Party registration is not required in Indiana, I'm not registered as a member of any party & I vote in every election.

In any case, the actual vote is secret.