Once I heard someone compare Eucharist to the physical consummation of a marriage. This idea stays in my brain for two reasons. First, well come on, it's gonna stick in your brain too now that I have said it. Second, because it answers a lot of questions and make some strange-seeming things make sense.
Compare joining the Catholic Church to getting married. There is a lot of preparation involved with both. I say this as a woman who was required to give up every Saturday evening for a year in my preparation to join the church. (I was only asked to prepare for a few months for my marriage.)
You have this whole physical two-become-one concept, perhaps with both. And there is this physical thing you do. In either case, if you explain it to a sixth grader they will tell you it sounds pretty gross.
In this context, however, it is easy to understand why everyone isn't invited to partake of Eucharist in the Catholic Church. There are a lot of very nice, good, probably holy people, who are excluded. But just as you shouldn't be going around consummating non-marital relations in the one way, the same is true in our relationship with Jesus and the Church.
A marriage involves a big commitment. You go through processes, you fill out paperwork, you make a public statement, you make a life commitment. Only under these circumstances can two really become one flesh and the system work as it should.
So the church asks for "date night" once a week and on a few major holidays. If you didn't show up for date night with your spouse it would not bode well for your marriage. This is one of the many reasons Catholics need to be present at Mass on Sundays.
I'm sorry that the Catholic Church seems like such an exclusive club and I hurt for those who through remarriage, mortal sin, or lack of understanding/interest are excluded. May the Lord heal our separations and divisions and bring us all together at the table soon.