I disagree in some part to this.The brain is the organ. It itself isn't illogical anymore than the heart is illogical. It functions.
Our thinking, our feelings aren't guaranteed to be logical or accurate or anything else. There would be no religion is that was the case.
What other feeling is illogical? Plenty. But I wouldn't characterize love as being illogical in most cases.
We are illogical when we buy lottery tickets. We are illogical most any time probabilities are involved. That's why "miracles" exist. We think the probabilities are too great for chance to account for it when that's not the case.
Is it logical for people to argue that Jesus arose from the dead?
We have no problem with being illogical.
I don't think love is illogical, nor any other emotion, but I guess that depends on how we define it.
Logic is the process by which we get from the inputs (call them propositions if you will) to the outputs.
If it follows valid logic then it is logical. Otherwise it is illogical.
To me love is just a proposition, an input, into whatever it is within our brain, our instincts, that give rise to the outputs.
So as such it is also not logical or illogical.
Furthermore, when it comes to human activity, what we deem logical or not is fundamentally based on the values we place on the various inputs into the process, and the goal we have set for that process. And is based on assessment of risks and rewards of actions.
You raise buying lottery tickets as illogical - but for some it is far from it: it is a matter of risk / reward... to the financially comfortable, who can afford to lose £2 a week and not even notice it, the risk is negligible and possibly non-existent, yet the reward of potentially winning £1m+ is huge, even if the probability is so low and the expected pay-out less than the bet.
One can view such things in pure numbers, and see that the expected return is less than the bet, and call it illogical to take the gamble. But that looks at just the one aspect, and ignores the risk of the gamble and the potential pay-0ff.
So it is not, in my view, illogical for such people.
So when we deem something logical or not, one has to understand what the propositions are, what the inputs are, what the values of those inputs are, what the desired outcome is. Only when the actions / decisions go against the goal you have set, taking into account the inputs and values, can we / should we deem something "illogical".
But I would say that love is just an input, and it may fuel the values we place on things, and woolliness of our thinking.
But it is the thinking that would be illogical, not love itself.