This is a very nice analysis and critique. It seems to me to be unavoidable. Perhaps I should fold my tent and be on my way. And although I can see you are right, all of a sudden I can't breathe - I'm suffocating.First, let's deal with the initial statements...
"If you can fall in love, does that mean you have a fully-functioning brain?"
"If you can fall in love, does that mean you're "whole"?"
"If you can't fall in love, does that mean you're brain-damaged?" <--
I'm obviously paraphrasing these... why? Just because psychology denotatively means "study of the psyche [soul]" doesn't mean the people who coined the word had proof that such a thing as a soul even exists for the sake of study. Many neuroscientists and philosophers would say that "soul" is merely a rough and fuzzy way of describing the personality as it derives from biochemical brain activity. So... maybe we're trying to measure the mass of a perfect vacuum?
Moreover, the two pronouncements by OP are begging too many questions... it's sort of like asking... "if you can ride a bicycle, is your body fully-functioning/unimpaired?" I might be able to ride a bicycle, have well-formed and non-diseased limbs, no inner ear infections to interfere with balance... and yet be color-blind... so my body is deficient... Likewise, even if we accept point blank the analytical robustness of a concept like wholeness of personality or soul and don't quibble about what love is... the statement assumes an invalid argument... I may be able to love, but I could be lacking wholeness nonetheless (perhaps I can fall in love but have no sense of reason; i.e. I am a madman who does mad things and, when loving, only falls madly in love...)
The second statement hinges on the first... but could be evaluated independently... just to counter it... maybe, provisionally accepting all the assumptions inherent in your questions... I am whole and am perfectly capable of falling in love, but I've never found the right person... maybe love is contingent on being in the right situation... so I satisfy the condition of being whole, 'being capable/able of falling in love', but the potentiality of being-in-love has never been actualized into actually-being-in-love... does wholeness require realization of all potential, or is mere potentiality enough to guarantee wholeness?
"falling in love means losing yourself in another person." I disagree. I believe that love in 'real life' doesn't fit one description... more importantly, I believe strongly that a good sense of self is important to the survival of a relationship between two people, especially when love is involved... I love my mother, but I don't forget myself because of her. And when I was in a deep relationship with a girl in high school, the love I felt I had partly stripped me of self-identity, insofar as I began to define more of who I was and what I wanted to do according to her, and yet I never lost myself... does that mean I wasn't in love? I don't accept that....
The whole world loves a lover... agreed... if it's an ideal lover.
BUT...in general, more needs to be done to define the terms in usage.