You are not alone. Literally thousands of bewildered students feel the same way.
The point of the advice, of course is useful, and at it's core simply means you need to articulate properly what you bring to the table, what you will contribute to a company, a team, a vision. But the connotation around this phrase is awful. The idea of "selling yourself" is uncomfortable to most people. In some cultures it would be considered downright tasteless. Most of us are told growing up not to brag, not be a showoff, not to boast. That doing so in fact undermines your accomplishments. But then, did anyone teach us how to talk accurately and confidently about our accomplishments without sounding like an a*s? No. Worse, most people - certainly most of my students and ALL of my international students - feel awkward, guilty, and embarrassed about this aspect of interviewing and networking, and so they end up undermining their accomplishments and candidacy anyway. They constantly question whether they're talking too much about themselves, or whether saying "I did X or Y" sounds like they're taking all the credit.
I get that. But we do have to figure out a way to alk about ourselves in a way that captures our value (we’ve touched on this in so many places, including here). I have seen hundreds of times one candidate have exactly the same experience (or less) than this other candidate, and the former gets the job because he/she weas able to convey whatever he/she did in a way that was attractive to the employer. We don't have to argue about whether that is fair or not, we are not here to re-wire the universe. Human beings that don't know each other have to depend on what is communicated to them. So how can you communicate in a way, that is both comfortable to you and effective in terms of what the other person needs.
Re-frame it. It's not about selling yourself. It's about service, about helping the organization. It is about providing the future employer with the information they need to make a good hiring decision. Remember there is a mutual goal: for you to get the job and for the employer to find a great candidate. So, it's not boasting to confidently put forth your accomplishments, to tell them "here's what I can do for you.. and I am basing it on what I have done before." In fact, it would be misleading to not tell them these things.
Let the facts speak for themselves. Stick to actions you took and link them to results (your own or the team's result) and state it neutrally. Then the facts, data, and numbers will speak for themselves. e.g. helped the team add 8% to revenue for that year by supporting senior staff with timely and well researched pitch decks.
So, in conclusion, if you don't like selling youself, that's fine. But re-frame it in a way that works for you. Not communicating this information confidently - on a resume, in a networking email, at an interview- is a disservice to everyone. and no one wins. Employers may miss out on hiring a great catch and you might miss out on great career opportunities. For more on Action -> Result resume language crafting check out the Careerly Resume Guide and the 200+ Resume Bullets to see real-life examples of showing off your skills without "showing off." For more on answering interview questions like "Tell Me About Yourself and "Why Are You the Best Candidate for this Job?" go to our youtube video channel.