A nice broad question to set the scene
I'm fairly new to roleplaying and I'm struggling with a valid reasons for both why and how a character would multiclass into another class independently - that is, on their own, without specific training from an NPC, temple, college, etc.
I'm currently playing a Rogue and I would like to multiclass into Monk, taking more levels in both Rogue and Monk in the future. The current campaign has not included a local monk temple/monastery where my character could seek training (to explain his new skills) and at this point in the campaign my character simply doesn't have time to sit in a cave for a few months learning from a (miraculously) passing grandmaster.
I'm familiar with the idea of classes as a metagame concept, so I can get behind the idea of new class abilities retroactively being part of my character's existing training. However, the sudden jump in abilities from monk levels - especially the AC improvement from Unarmored Defence - seem like such a huge change for a rogue.
Most other classes 1st level abilities make sense to an extent, and can be explained away as a gradual improvement of skills that eventually "click" and makes a noticeable difference to the character. However, I can't quite resolve why someone used to running around in leather armour would decide they'd do better without it? Or why a rogue used to stabbing people in the back would start (effectively) lashing out with fists, elbows and kicks.
Paraphrasing the PHB slightly, Monks are portrayed as ascetic communal hermits, training for years to achieve personal perfection through the study of Ki. Multiclassing into the Monk class seems to ignore this whole background concept almost entirely.
So what roleplaying options/ideas are available to me in this scenario to explain my character's sudden acquisition of new skills?
For more character background detail (as discussed in the comments below) my character concept so far is a wood elf Assassin Rogue/Shadow Monk. I'm not aiming for a stereotypical street-wise city thief - instead I'd them to be more of a sneaky forest dweller (due to being a wood elf), killing only when necessary and intent on personal training and perfection. A sort of good/neutral "nature's ninja" if you will.
My character may also be taking a single level in Fighter at some point but this is a lot easier to explain simply through a personal focus/dedication to general martial training.
Bonus points are available for relevant or interesting concepts and ideas based around other classes outside this scenario, however, my main focus is explaining the Rogue -> Monk transition.