If you have to move on, you have to move on - but as others said, do it honestly... and tactfully.
When you dish out the excuses, people see through it anyway - as guild leaders and officers, raid leaders, etc. we've heard all the excuses before.
You can be direct and still be tactful about it. "
You guys are great & I've enjoyed my time with you, but I need more out of the game" works much better than an excuse that they see through, or people find out later was bogus.
Most people will get over things in time - especially if you make a point to be considerate.
There's a huge difference, IMO, between being flip about something and not giving a shit vs. setting goals for yourself and reaching them.
In some cases, btw, it's better for *both* sides if you move on. I have one friend that, when he's guilded & raiding with us I can feel the impatience coming off him in waves.

He wants a heavier raid schedule, contesteds and to be at the head of the pack, while we want the lighter schedule and to get there at a more relaxed pace. That vibe off of him gets me all wound up & makes me edgy and impatient myself.
I treasure his friendship and I miss him dearly when he's not around - but while I'd love to see him wearing our tags and at home in them, it is far better for him to be raiding somewhere that he's getting what he wants, than with us and dissatisfied.
So all that said, if "true" friendship is supposed to be at the core of things here - treat them like you would true friends: be honest, kind, and considerate when you have bad news to tell. Then give them time to get over it. After that point, things will work themselves out if they're meant to & what tags you have over your head should not matter.