Here is my thinking …
Resumes—first and foremost—must be truthful and should not mislead the reader in any way. Having said that, I do not believe you have to include all past jobs you have ever held on your resume.
For example, you might leave a job off your resume if:
The job is dated. Some people include every position they have held since entering the workforce. Even if you are mid-career or beyond, a new employer will only be interested in what you have done over the past ten or fifteen years. Older jobs can easily be left off your resume.
Your time at the job was brief. If you worked at a job for less than six months and it is not directly related to the job you are applying for, you might leave it off your resume. Leaving it on could raise questions about why the job did not work out for you and might portray you as a job hopper.
Your work was part-time, short-term, or contractual. Many people do term work while seeking full-time employment. You don’t need to list all these roles. However, if you wish, you may group them under one heading called “Contract Work,” which signals that you were not sitting around doing nothing.
You took the job to generate extra cash. A short-term job that helped you pay some bills while you sought full-time work can likely be left off your resume.
Having said that …
You should never omit relevant jobs (or any information) from a resume that will cause an employer to be misled in any way.
In particular, you should never omit a job to hide bad experiences. Even if you were fired from the job or left on bad terms, you should still leave them on your resume. Leaving them off will undoubtedly backfire on you.