This happens not only for "愛してる" For example, when we use "have" in English, we say "I have a book," but we usually don't say "we are having a book," right? However, in Japanese, people pretty much use "I am having a book" to express "I have a book" of English. And expressing "love" is not an exception of this rule. When people say "I love her", people say "I'm loving her" in the Japanese grammar. This is why "ている" often appears in Japanese language. Examples, (1) 僕は本をもっている。 In Japanese grammar -> I'm having a book. In English grammar -> I have a book. (2) 私はあなたを愛している。 In Japanese grammar -> I'm loving her. In English grammar -> I love her. (3) 彼はAを知っている In Japanese grammar -> He is knowing A In English grammar -> He knows A If you get a little deeper of this things, you would find a lot of more similar examples like above. I think that this issue occurs from the difference of two different languages or cultures. ;)

ーーーする　is the active form of verbs. ーーーしている is the progressive form of verbs.