Wontleave, you said: " I don't see anywhere in Scripture where every Christian is supposed to partake of the emblems."
- Jesus told the Apostles to eat the bread and drink the wine and commanded them to do this in remembrance of him.
- Jesus told the Apostles to instruct the disciples - all of them - to "observe all the things I have commanded you". That would include eating the emblems.
- Paul showed that Lord's evening meal was taken by all Christians without distinction, just as Jesus had commanded. Paul obeyed Jesus command at Matthew 24, just as the other apostles did, and instructed all Christians to "observe all the things I have commanded you" - but Paul phrased it this way "For I received from the Lord that which I handed on to you, that the Lord Jesus in the night in which he was going to be handed over took a loaf and after giving thanks, he broke it and said this means my body which is in your behalf. Keep doing this in remembrance of me."
To partake of the emblems is to accept that Jesus died on your behalf - "this means my body which is in your behalf". To not partake is to reject his sacrifice. This is also very explicitly stated in Scripture in John 6 where Jesus says "Unless you eat the flesh of the Son of MAn and drink his blood, you have no life in yourselves. He that feeds on my flesh and drinks my blood has everlasting life, and I shall resurrect him in the last day. For my flesh is true food and my blood is true drink. He that feeds on my flesh and drinks my blood remains in union with me and I in union with him. Just as the living Father sent me forth, and I live because of the Father, he also the feeds on me, even that one will live because of me. This is the bread that came down from heaven....he that feeds on this bread will live forever."
It couldn't be more explicit.
No partaking. Not in union with Christ. Not a Christian. No life.