We all, particularly women, tend to downplay what we're actually good at. When somebody compliments us, we demur. And I definitely include myself in that. I don't want to seem too vain in accepting a compliment. And it's true, I think, that bragging can go too far.
And I do feel a little silly taking credit for things that come really easily to me. Like if somebody is impressed with, oh, my ability to tell you what note you just played to me. Seriously, that's just a little quirk of my brain that I have nothing to do with. It's like complimenting me on having pretty eyes... I mean, glad you appreciate them, but I didn't have anything to do with the process of them being so.
BUT. There are things that I've worked hard on and am good at.
Now, I think there's something interesting to be said about what you can and cannot take credit for, and what taking credit should mean ... but in the meantime, some things I do take credit for:
In my life, there is one thing I have always strove to do for myself, that I believe is among the most important things one can do: I have tried to be right for the right reasons about what is true and not true. There's a lot of people in this world who don't put in the effort to filter mistakes and lies out of their beliefs; and, conversely, there are people who trust their logic to take them everywhere regardless of the difficulty of real problems. I know I make a lot of mistakes, but that's the thing: someone who knows they make a lot of mistakes will persist in a lot fewer mistakes than either the idiot who doesn't try or the crank who drives the mistakes onward to their ridiculous conclusions. I'm smart enough to hit what I aim at, and wise enough to double-check what I'm aiming at.
A second thing: I've always been helpful. I may be literally running to catch the bus and stop just to point a complete stranger in the right direction to get where they need to go - I strive to always be the one who does right by the people I meet.
And speaking of Scout virtues, I aim to be prepared. Just to give a taste, my backpack contains measuring tape, masking tape, Scotch tape, electrical tape, duct tape, cotton twine, glue pens, ball-point pens (black, blue, and red), Sharpie markers (black and red), mechanical pencils and spare leads, post-it notes, pocket calculators, an LED flashlight, a first-aid kit (including gauze and medical tape), and quite a variety more, even before you open the main compartment (where the towel is). I have used some of this for myself, on occasion, but I am as free with this material as I am with my time, for people who need a hand.
Back to what's in my own head: I've got skills, dude, and I don't just mean the car-racing video games (although I'll give you a run for your money there, too). Besides the basic outdoors skills and leadership skills that the Scouting program instills, I can take credit for quite a bit of my academic accomplishments. The least of these is my coding chops, which won't get me a paycheck any day soon but which will more than suffice to solve partial differential equations given initial and boundary conditions - and I know enough to know how to catch errors when I solve them. As for setting up these PDEs, I've aced my way through all the basic maths education underlying them and, in parallel, studied the full breadth of what Newtonian mechanics can analyze under a variety of circumstances and assumptions. And I know enough to know how to avoid solving these equations, to know how to laser in and find the results on the level of experimental solution, without going wrong.
I can convey this knowledge, too. The worst kind of teacher is the one who doesn't know their material, and the second-worst is the one who doesn't know that their students don't know - and I know. One-on-one, anything you don't get I can give you, and give you a list of problems to work as well; and in front of a class I can lead you every step of the way from setup to solution, and tell you from whence every jot and tittle derives.
And it's a two-way street. I won't swear to remember your name tomorrow, but I can follow the implications of your theorems as well as you can, fast enough to know the difference between a subtle point and a careless error between your writing it on the chalkboard and I in my notebook. Ask me for feedback, and you can rely upon me to return with useful questions and comments.
I'm sure I could say more, but at 1:05 in the morning it might be better to stop here.