I honestly fail to see the problem. 
My kitty is turning 10 and I have never loved an animal as much as I love him.
He was born premature, I had to feed him with a bottle and spend lots of nights awake with him, but it all was worthwile for the love I have gotten from him.
He is a bit of a scardy cat and the move to a new house stressed him out and in turn also me, but here we are sound and happy in our new home.
I can write pages and pages about him and how much he means to me and his personality and the joy he brings me (and yes I do speak to him and he does speak back). So as you can gather I am a cat lady.

I love my cat and that can be a real curse sometimes - my love for him will keep me from going on holiday, or going and wanting to come back on the 2nd day.
So I guess you can say it is not normal, but I am the type of person who looks in an animal's eyes and see a soul. So judge me if you like, I love being an animal addict.
I believe a lot of people will understand this and the feeling they have for their animals and that they consider them as part of the family - for you I say "hats off"
I will not speak about people who does not love animals or abuse them - you are not worthy of being mentioned .... just know there is a special place in hell for you.
I love all animals and will not even kill a spider. I will freak out about creepy crawlies but will rescue them with a glass and a paper or something to be able to put them back in nature. (and maybe hurt myself in the process by pulling a muscle or two hahaha)
My motto is simple - if you treat children, old people and animals with love and respect, then in my books you are a good person. <