He never ordered it to be celebrated nor did he teach it to his Companions. Based on this, his companions did not celebrate it either. The companions are the most knowledgeable of people concerning his sunnah and were also the most loved by him. However, this was not the case. Not one of the scholars of the first three generations celebrated his birthday and they did not order it to be celebrated.
Every invented matter is an innovation and every innovation is a misguidance.
There is no categorization of innovations into good and bad. All innovations in the religion are evil and forms of straying from the truth. Avoiding Bida'a is one of the most important principles of the Sunnah. We are told to have hatred for innovation, keep away from it, warn people about it, and to refute the innovators which is for the Ulemah alone. They do not love them and they do not keep company with them.