As an active secularists I fully support a movement to try and remove words that have religious connotations and "soul" is a biggie. I prefer to term it inner being or even personality.
Answer to the first part: I agree. However, one special mate can have attributes that enhance the relationship yet at the same time other relationships can have attributes that can enhance the relationship in a different way; no one way is the perfect way.
Of course animals have personalities and the more sentient the being the more pronounced the personality. I have had cats and dogs and each one had a distinct personality. I live across the street from a pony farm. Right now there are 4 donkeys that reside there. When a car passes the farm each one responds in a different way in a different voice (people who have heard this always remark: what in the world was that)? Has anyone heard crows? I have noticed there are some that literally talk to others in an unmistakable way. I will stop and listen and wonder what they are saying.

I can see your point and raise it can an animal be a soul mate

I believe YOU used the word "soulmates" and yes we can haave more than one

I do believe in the soul mate concept. I have had many relationships and actually thought the last one was my soul mate. The concept wasnt proven false, my choice in Dawn was.

I have worked with and trained animals all of my life, mammals have varying degrees of awareness, emotion, and problem solving abilities. They also display varying level of individuality what some people consider as there "personality". They also form relationship with other animal within their species and outside of it. As their intelligence increases they abilities to overcome basic instincts increases but so, do their emotions.
Birds are very different than us mammals their minds work far differently: problem solving abilities are generally much greater as are their responses more affected by instinct. They, too, display uniqueness.
As for the concept of soulmate, I agree with you a soulmate is just an extremely compatible individual to you.

Yes, I don't believe in souls or soulmates, but I do believe that many animals are closer to us in self-awareness and emotional richness than many of us give them credit for. I am fascinated by communication with Koko, evidence of elephants' grieving, and the recent discovery that dolphins have names in their sonar language (i.e., a particular call sequence that always refers to a particular individual).