I've recently learned that this quote comes from the movie "Love Story". It's a phrase that has always perplexed me. Sure actions speak louder than words but that doesn't mean that words don't play a part! You need both actions AND words!
Just because you love someone, doesn't mean you will always behave in a perfect way towards them. We are all human after all. So if I do something wrong to a loved one, why shouldn't I be expected to say sorry? Even if that person tells me "don’t worry about it" or "you didn't have to say anything" we both know that yeah, I really DID need to say sorry.
And if you really love someone, and you've hurt them by something you've said or done, wouldn't you want to clear the air by saying sorry? Sure, we don't NEED to, it's not like the other person is not going to love you back forever, but it sure does help if you can vocalise as well.
Words without actions are empty but actions without words are also lacking.
Bottom line, be good to each other!