Anyone knows the reasons why 13x13 has been chosen as a standard format instead of 15x15? I think 15x15 is much better because the territory line stands on the 3rd line instead of the second on 13x13. Also the points in the center are less on a 13x13.
Overall I think the 13x13 format can create more bad habits than 15x15 or 9x9.
What do you think?
I’m still not sure why this “territory on the 2nd” saying for 13x13 and 9x9 is so popular imo. The reason third line is territory is cuz it’s really easy to make a base on 3rd line, and there usually aren’t invasions under it, unlike 4th line. I know that this is usually backed up by the diagram, but that’s more to explain that territory and influence are of similar value on 19x, and even then I question its usefulness in really showing anything (as influence rarely does anything near as nice as make a huge central moyo).
But the best explanation I’ve found is that 9x9 has 81 points, 13x13 has just over double that at 169, and 19x19 has a bit more than a little over double that 361, making 13x13 a nice “middle” ground, and I typically like to hypothesize that for handicap 1 stone 9x9 = 2 stones 13x13 = 4 stones 19x19, which is a nice little conversion (assuming it makes any sense)
As for habits… eh… I typically suggest playing on 19x as soon as it’s comfortable. 9x9 is there to teach tactics while you get comfortable with the game, 13x13 teaches some of the basics of whole-board strategy while not intimidating the new player too much, and 19x19 is where the serious games end up happening. But if 19x19 isn’t intimidating you can just skip right past 13x13 imo. Just get used to the territory/influence balance you’ll be playing with for most of your go career anyway.
Good observation on the doubling of intersections! 
I’m inclined to just blame it on tradition. You can form bad habits on any board size besides 19x19, if your end goal is to play well on 19x19.
Beginners, don’t be intimidated!
You can play your first game on 19x19 if you want to.
https://senseis.xmp.net/?15x15Board
If you’re in the mood for composition, feel free to improve this five-year-old SL stub.
I’ve heard 19x19 can be pretty nice
And lose out on the most fun board size? Heck nah! 
Personally I like 9x19.
https://katagotraining.org/sgfplayer/training-games/5364455/
As a computer player, I prefer 19 x 9