>apply for a job
>actually match all the requirements posted
>sorry but you don't fit our profile
what did they mean by this?
They could have someone losing their shit at them for saying they were not worthy of the job. Not that it's likely, but if you could avoid it, you would. And the lower the position is, the more likely it is.
Remember that your qualifications written on paper are not the only things that matter.
How well are you able to hold conversation, some psychological profile, etc. are huge factors that are considered when hiring.
Meeting the qualifications is meeting the standard to give it a shot. Unless you're in an extremely competitive field, everything else boils down to the vibe they get from you and how well you do the interview.
Basically this is a euphemism of saying that you're not the kind of employee they are looking for. That can mean wildly different things depending on the workplace. Maybe you seemed to answer impulsively and without thinking it through during the interview and they are looking for someone who is diplomatic and discreet and can't picture you being that person. Maybe you were extremely neutral and soft spoken and they have a bubbly, creative person in mind.
Don't forget they don't just know the job description but also the day to day reality of working said job, the people you would be working with and so on. They can see how you'd fit into the company, the team, the specific project. That goes beyond certain skills or background information.