I sometimes wish singing teachers sat in on each other's lessons, like normal classroom teachers and (presumably) sports coaches as well, since what they do involves bits of both. I understand that every singer, and hence every teacher, will approach singing differently, but sometimes it's quite worrying how little common ground there seems to be both in what they say and how they say it.
They all agree on some things, but usually not in the methods to achieve them. The only two I can think of that are completely uncontroversial are that you have to sing with a lifted soft palate, which after all is what distinguishes classical singing from other kinds, and that unless you are a countertenor (or very young) there should be some sort of involvement of the muscles in your lower thorax & abdomen, ie 'support'. Everything else - which muscles, exactly, are most important? Should they all be tensed all the time, or only some, or only for certain parts of your range? - is up for grabs. Annoyingly, there are also some principles, like 'when singing, you should not feel that your voice is coming from your throat, or feel any pressure there' which teachers agree on but differ on how to achieve, or even when it is actually happening with a particular pupil.
So both of the teachers were very good and had some valuable new insights, but they and A are all poles apart in what they think I should do to sing better. In a way I knew that already: when you find a new teacher it seems at first that they can solve all your problems and you make rapid progress, but eventually they have taught you most of what you can learn and you need to try another approach. A and I have agreed we've reached this point, but this is the first time I've actually had to find a new teacher on my own initiative, and I want to make the right decision. Oh well - I'm sort of in limbo at the moment, but it's quite fun in a way.