A home church is just a group of folks who hold regular church services in a home verses a traditional church. Often this is the beginning of a church start and it often moves into a church in a regular facility whether it be a traditional building, store front etc.
The house church movement is rebellious because they reject the biblical instruction on church leadership. They do not like preaching of any kind and use pejoratives to characterize it. They do not like leadership such as pastors and again use pejoratives to characterize them. Since they reject the biblical format for church governance they are also ungodly and as the author of the op has well shown they rebellion almost always breeds arrogance.