The explanation is confusing indeed because closer means not only "brighter" but also closer. But we can try to overcome this confusion by a thought experiment:

The explanation is confusing indeed because closer means not only "brighter" but also closer. But we can try to overcome this confusion by a thought experiment: lets compress Andromeda galaxy by a factor of k and divide distance by a factor of k. This way it would be k times close but it would have the same angular size. And now lets figure what the k need to be to make Andromeda this bright. Does such k exists? I believe it does. I'm not sure would it work, because my physics knowledge is limited, but if I'm right then it is a non-confusing way to interpret the confusing statement "needs to be closer to be brighter".