Why exactly do we believe in God even though there is no empirical evidence for His existence as far as we know?
I do not understand the question. Something that is empirical is based on experience
, so if you experience God, you have empirical evidence of Him. The whole idea of empiricism as an epistemic system is that we trust our senses (as in, our sensory organs) as the route to knowledge. That's a Biblical idea, believe it or not -- remember how our Lord Jesus Christ deals with St. Thomas' doubts in the Gospel of St. John (chapter 20, verse 27)? Then He said to Thomas, “Reach your finger here, and look at My hands; and reach your hand here, and put it into My side. Do not be unbelieving, but believing.
Of course, Jesus Christ also says in the Holy Bible (only two verses later) that blessed are those who have not seen and yet have believed. What a paradox, eh? If you think about it a little bit, you might even come to the idea that empirical evidence (experience) and faith actually work together.
I oftentimes hear people here making fun of Scholasticism and acting as if there were some blatantly obvious grand error about it, when in reality, they never explain what is wrong with it or why.
I will take a stab at it, then, even though I was never very comfortable with it myself: One of the problems of scholasticism is that it is actually a reduction
of experience in favor logical proofs and inferences divorced from any kind of necessary sacred context (such as we experience God in the Liturgy, for example). "If P, then Q" is fine and all, but we need to always remember that God is not a variable in an equation that some smart guy dreamed up somewhere with his God-given
Why believe in God if there is no logical reason for His existence?
Because we have experienced His presence, or, probably more honestly, we need to. It's what we were created for.
Truth is, we won't even ever find evidence for His existence in the natural world unless He blatantly talks to us or interacts like we hear about in the stories of the most devout Saints who've experienced the Uncreated Light.
What exactly is so wrong with demanding a good reason to believe in God?
A better question is who decides what constitutes a "good" reason. I have tons of good reasons, but they probably won't convince someone who isn't me.
It seems like in religion, demanding a good reason or faith with seeing is considered taboo or looked down upon. Why? Isn't it more virtuous to seek reason than to accept something with no good foundation?
Again, you are using these terms as though we should all have agreed-upon definitions of what they mean. 'Virtue' is a tough one. The Desert Fathers teach us that the greatest of all virtues is humility, and it seems like humility might be better expressed by trusting in God through doubts and troubles than in elevating your own reasoning capacities and personal opinions of what is good above the wisdom of the Apostles and the Fathers.
People often try to answer these questions with odd, romanticist existential arguments about having a "relationship" with Him or something having to do with their feelings and emotions, but none of these really cut it or make sense. How do you "have a relationship" with someone who doesn't interact with you?
Leaving aside the language used to express it, what do you mean that God doesn't interact with you? Especially in Christianity, God interacting very directly with us (and we with Him) is kind of a huge deal. He became incarnate and walked among us and was crucified for us. We eat His flesh and drink His blood at every liturgy. At the risk of being pelted with e-tomatoes for using an odd, romantic word (even though I don't mean it in that way here), I think that this is the most intimate interaction that is possible with anyone, ever.