I have a toddler boy who is one year and eight months old. He is my first child. Recently he is learning to speak. I noticed that when he hits family or other toddlers, no matter knowingly nor unknowingly, he refuses to apologize. Even worse, he will break whatever he holds in his hand and then cries. I don't know why he is like this. What should I do to let him know he has hurt someone else and he should apologize? I am worried.
You are expecting a toddler to act as an adult. He isn't able to communicate well, of course he doesn't apologize. Likely he doesn't even know what an apology is.
When he hits someone, you immediately slap the hand that he used and tell him firmly, "No! Hitting someone is not allowed!" He will cry, but soon stop. You meanwhile go about your business, but keep an eye on him. You need to be consistent about this because you allowed him to develop the habit to hit, so he is going to experiment to see when hitting is allowed. You cannot punish him sometimes and sometimes not. He will get confused about the rules if they are not consistently enforced.
The same rule is used when he breaks something.
When he gets older, say around 3, you can introduce him to the concept of saying "sorry" when he does something wrong.