This question reminds me something I used to be asked a LOT when I was doing fitness: can I build muscle and lose fat at the same time? Well in total honesty and from my humble experience, our body doesn't like to do more than one thing at a time. To some degree you can become flexible and strong, but I don't believe the two can happen together, you'll have to work first on passive flexibility (lengthen), then on active flexibility (lengthen+strengthen). Working only on active flexibility will not deepen your stretches, but control them better. First off let me define what active and passive flexibility are: active flexibility is "the ability to assume and maintain extended positions using only the tension of the agonists and synergists muscles while the antagonists are being stretched", like for example lifting your leg as high as you can, with no help from your hands. Passive flexibility is "the ability to assume and maintain extended positions using only your weight, the support of your limbs or some other apparatus (a chair, blocks etc)", splits on the floor are an example of passive flexibility."Research has shown that active flexibility is more closely related to the level of sports achievement than is passive flexibility. Active flexibility is harder to develop than passive flexibility; not only does active flexibility require passive flexibility in order to assume an initial extended position, it also requires muscle strength to be able to hold and maintain that position."
I believe active flexibility works best with those who already have good flexibility foundation and actually need more muscle strength and control for their sport, or they tend to be more supple than average people and unstable in the joints so strengthening is a priority (kids are the perfect example). Passive flexibility works best for everyone else who lack muscle suppleness and the ability to relax (tend to be stiff -->most adults, over 20-25 yo). If you're starting out as an adult I'd learn first how to RELAX your muscles with passive stretches, create space, lengthen, learn how to breathe and let go of unneeded tension. Adult bodies are stiff and active flexibility alone won't increase dramatically suppleness, I'm not saying it wouldn't work but I would integrate it later on when a basic foundation of passive flexibility has been established.
Me in passive stretching, oversplit on couch
and active, from standing going into bridge