For the simplest of reasons, by going to a dedicated fitness center where there are public who are also coming for the same reason, you get a feel of life a part of a healthy society and moreover there are instructors and specialists to guide you to a better workout, focusing on your strengths and weaknesses. It’s like going to school every day and live a part of the discipline and learning things to be a better personality.
Even bad gym from your neighborhood provides facilities too that you won’t get at home easily without spending too much. It’s better and rational to join a sports center rather than spending heavily and afterward lacking that enthusiasm to use them. So, get a reasonably priced membership rather than spending irrationally.