If the option to add a particular country to your alliance, it's either because you don't have diplomats; you already sent that country a diplomat in the last month; you're not the alliance leader and have no right to decide who else joins it; the target country is already in an alliance; or - the one you're most likely not to notice - the target is a vassal of another state, and may not join any alliance.
If they are refusing to join, it's because there is at least one country in the alliance that they do not like. Contrary to above opinions it is possible to create large alliances (I've had seven, others have reported eight or even nine countries at once) but it becomes exponentially more difficult: if there are already five countries in your alliance, your new target country must like all five of them before it will accept the offer.
There isn't much point creating such large alliances anyway, because they almost always shatter as soon as any member gets involved in a war somewhere.