Re: "following Christianity. Jesus didn't say, "follow Christianity"; He said, "follow me." That is a big difference, and if you can't see that, nothing I can say will help clear it up."
I'm suspecting equivocation on your part with the term 'Christianity'. Christianity is the following of Jesus. Where a group strays from that does not represent Christianity, but rather represents aberrations of Christianity. Jesus appointed apostles to establish churches which were commissioned to spread Christianity. Would you reject the writings of the apostles merely because they weren't written by Jesus directly?
Re:"Yes, there are many false Christians, in all sects that proclaim themselves to be Christians; why is that any kind of surprise."
The question is: "How do Christians deal with that?" historically, you can look at the early church fathers, some of whom were students and friends of the apostles hand picked by Jesus, and you will see that they 'argue' for their beliefs. There are volumes upon volumes of arguments for Christianity from the early church fathers.
Re: "Contending for the faith means being faithful. Just follow Jesus--"
This idea that contending for the faith does not include interaction with and correction of false ideas is completely foreign to Jesus, the Bible, The apostles, and Christianity. Maybe you should take your own advice and stop arguing for your view. That is not what the apostles modeled. They wrote letters to churches correcting their errors and sins with written arguments. Read the New testament, it is full of contention against ideas in opposition to Christianity. Most of the books of the new testament are letters sent to churches which are primarily theological and moral corrections.
2nd Corinthians 10:5 "We destroy arguments and every lofty opinion raised against the knowledge of God, and take every thought captive to obey Christ,"
Jesus similarly corrected pharisees and such. You say to just follow Jesus, but it's as if you want people to turn a blind eye to what Jesus actually did and taught his apostles to do. What kind of following is that?