An "antagonist" is just someone who gets in the way of the protagonist reaching their goals. Someone can be an "antagonist" without also being a "villain". (And even villains often have some good qualities, or well-intentioned motives or logic behind their actions. The majority of "bad" people aren't just "evil for the sake of being evil"; there's a reason they do what they do, and they may even be convinced that THEY are the good guys).
Examples:
Protagonist is a teenage boy with a crush on girl. Her father is a great dad who loves his daughter and has a good relationship with her, but he refuses to let his fifteen-year old daughter date yet because he thinks she is too young to be in a romantic relationship. Maybe he even likes and gets along with the protagonist. But he says "no way no how are you dating my daughter at this point in time." The protagonist's biggest wish is to go out with the daughter. Hence, the father is an antagonist, but not a villain. A little over protective perhaps, but most people would consider him to be a decent guy anyway, including the protagonist. Regardless, the fact he is getting in the way of the goals and journey of the story's protagonist makes him an antagonist.
Protagonist is a young man who wants to marry a young lady. Her father lost his wife and older daughter, who he doted on, in a horrible accident and has become fiercely overprotective of his remaining daughter. Even though she is twenty years old, he barely lets her out of his sight, micromanages her life, and refuses to let anybody who threatens to "take his daughter from him" near her. He is willing to go to any means necessary to "protect" her, including illegal means like blackmail. He despises the protagonist and even, at one point, attempts to kill him. This father is also an antagonist, but would also be called a "villain" due to his willingness to do things that most people would consider immoral or reprehensible. But in his mind what he is doing makes sense: He loves his daughter, wants her to be "safe" and is willing to "sacrifice" anything to ensure her physical welfare. It doesn't even occur to him that in focusing so single-mindedly on his daughter's physical safety that he may be harming her in other ways.
Edit: Something interesting can occur is when the story's protagonist is also a villain! In this case you might have a story where many of the story's "antagonists" are "good guys", because they are trying to stop the bad things the main character is intent on doing!