You could do what I did and obtain a starter and trainer’s license behind their backs, leave them a note, and run off, only to contact them almost a year later after you’ve figured out what you wanted to do with your life through a series of exciting adventures that bring you closer together with your pokémon.
Bill! —LH
Or alternatively, parents can often be difficult to convince, as they typically believe they know what’s best for their children. Not saying that the majority of them don’t, of course! It’s simply that parents (the good ones, anyway) often worry, so many of them are reluctant to watch their children take considerable risks.
With that in mind, though, it’s certainly worth it to try. A trainer’s journey is about discovery, both outside oneself and in, and that may be a good thing to remind them of. You simply need to be strategic about it.
First, come up with a plan—one with concrete dates. You’ll need to tell your parents exactly how long you plan your first journey to be. For example, consider telling them that you’ll spend a year as a trainer (this is roughly how long going through a single league circuit takes anyway) and that afterwards, you’ll contact them, and the three of you can discuss what your next plan of action is. Include a promise to keep in touch periodically—either once a week or whenever you reach a new pokémon center, whichever would be more comfortable for you to follow through with. Giving them a timeframe reinforces the idea that this is a temporary part of your life, that you’re simply trying out new things, and that becoming a ranger is still very much an option for you. The latter especially will make it easier to reason with them because you’re opening up an avenue for compromise down the road.
Additionally, do a bit of research into the logistics of a journey too. Think about how much one would cost and go in with a rough budget. I know that seems a bit overboard (especially if you’re the minimum age for obtaining a license), but telling your parents that you plan on being responsible with your money or responsible in general (through showing them that you’ve thought of these things) will also help them relax when it comes to the idea of letting you take care of yourself on something as exciting as a journey far from home. Here’s the part where you can also bring up the fact that training will teach you how to interact and handle pokémon, which are essentials for becoming a ranger anyway.
Of course, it wouldn’t also hurt to actually be more responsible. Helping out around the house without asking or taking small jobs around your neighborhood (but preferably both of these things) will show your parents that you have the sort of ambition, motivation, and responsibility you’ll need out there on a journey.
Above all else, though, when you do sit down to talk to your parents, do so as an adult: level-headed and willing to negotiate. Chances are, your parents will be far more willing to compromise or even relent if you’re confident enough in your arguments and you’ve come in with a thought-out plan.
Best of luck!
(As a note, yes, this doesn’t work with all parents. Some are indeed not the sort who can be reasoned with, but your situation sounds like it might not be the case.)