भक्त्या मामभिजानाति यावान्यश्चास्मि तत्त्वतः।ततो मां तत्त्वतो ज्ञात्वा विशते तदनन्तरम्॥
bhaktyā mām abhijānāti yāvān yaś cāsmi tattvataḥtato māṃ tattvato jñātvā viśate tad-anantaram
Word by word
The verse says
Through love he comes to know me as I am and how much I am. And then, knowing me as I truly am, he enters me straight away.
In plain words
The order is stated outright here, and it is the opposite of what you would expect.
Love comes first. Knowledge comes out of it.
Not: understand, then love. Rather: love, and then you understand, because this is the kind of thing that does not open to inspection from outside.
Where you've felt this · in relationships
You can read everything written about a town and know the rainfall and the population. Then you live there for two years and someone asks what it is like, and you find that almost nothing you knew beforehand is in the answer. The facts were correct. They were not knowledge of the place.
Going deeper
Knowledge through love rather than love after knowledge is a claim about what kind of thing can be known from outside.
Some things yield to inspection. You can learn the melting point of a metal without any relationship to it. Other things do not work that way at all. A person, a piece of music, a place: these only open to someone who has committed something, and the commitment is not a bias that distorts the knowing. It is the instrument.
That is the claim being made here. Devotion is not a reward for having understood, and it is not a substitute for understanding. It is the means by which this particular object becomes knowable.
Which also tells you why argument has never settled anything in this area. Nobody has been reasoned into it, and nobody has been reasoned out of it, because the question was never being decided by the faculty that argues.