[c] Comparing user-inputted characters in C

Because comparison doesn't work that way. 'Y' || 'y' is a logical-or operator; it returns 1 (true) if either of its arguments is true. Since 'Y' and 'y' are both true, you're comparing *answer with 1.

What you want is if(*answer == 'Y' || *answer == 'y') or perhaps:

switch (*answer) {
  case 'Y':
  case 'y':
    /* Code for Y */
    break;
  default:
    /* Code for anything else */
}