The citation you quote is from the French Renaissance essayist Michel de Montaigne who is said to have influenced many posterior authors ranging from Descartes to Shakespeare.
It is originally written in old French and is part of his essay titled "Of Friendship". Here is the exact citation:
"Si on me presse de dire pourquoy je l'aymois, je sens que cela ne se peut exprimer, qu'en respondant: Par ce que c'estoit luy; par ce que c'estoit moy."
Chicago Univ - page 188
It is not about love but mere friendship and applies to his best friend Étienne de La Boétie 1.
A better although not perfect English translation would be:
If a man should importune me to give a
reason why I loved him, I find it
could no otherwise be expressed, than
by making answer: because it was he,
because it was I
This apparently simple quote has come down to us because of its density. As you have understood, its deliberate simplicity is a powerful way to convey many complementary strong sentiments. I've outlined below a few of them.
Comprehensiveness. Whereas some people will say "what I love in you is...", thereby implicitly suggesting that the rest of the personality of the loved one is less attractive, Montaigne suggests that he loves all and everything about La Boétie. This comes from the part "Because it was he" in which "he" is taken as the simplest way to mean "all of his person".
Mysterious alchemy. By explaining nothing about their reciprocal attraction, Montaigne suggests that it is beyond rational understanding. This is prepared by the apparently unnecessary but actually powerful introduction "If you press me to say why I loved him, I find it could no otherwise be expressed than by making answer...".
Reciprocity. The first part "because it was he" is nicely balanced with the symmetric clause "because it was I" suggesting that the feelings were shared.
Perfect fit. In the same way this very balance "because it was he" and "because it was I" transcends the simple notion of reciprocity because it suggests a perfect match between both persons. The intended meaning is: "there is no more way of explaining why he liked me either".
Predestination. This perfect match in turn ultimately implies the notion of predestination. He and his friend were bound to meet and mutually single each other out one day. As a consequence, the mutual attraction was irresistible. In another passage he also suggests it was a case of "love at first sight".
You could probably find more ideas in this simple phrase. Its deliberate simplicity is a powerful way of suggesting many interpretations.
Montaigne and la Boétie were separated by the latter's untimely death but both friends are now reunited in the way their respective streets are located in Paris. Rue La Boétie and Avenue Montaigne are two of the most well-to-do streets in Paris and are linked by the "Champs Elysées".