Will a journal reject my paper just because a grad student is the sole author?
Publishing paper does not necessarily need co-author and supervisor. However, it is strongly recommended. Having experienced co-author (not another unexperienced author) with couple of publications like your supervisor has several benefits, including:


Your co-author reads paper and puts effort to make it more professional and  mature for publication. He/she checks to ensure there is no mistake in technicality, presentation, and English.
It gives more confidence to reviewers to ensure that what you did is scientifically correct and is also producible. Though rejection of papers with several experienced authors is also a very common issue.


In research, there are several small hints and tiny things to consider that can impact on the final results/outcomes of the research. If you submit without your supervisor/advisor's, particularly without his help and actual supervision, it is very likely to have those error.

In reality, research is very much complex, though it might look very simple. There are many many things to consider before undertaking research, reporting it, and even trying to submit it. Thus, your idea might not be yet ready for publication yet. Your supervisor may want to help you do not get a quick rejection that discourages you.

I don't think that exist any supervisor on the earth that avoid publishing paper unless there is either threat to its credit or the work is premature. Your supervisor may exaggerate on the quality of your work/paper though it is not yet mature enough to encourage you. So, if he admit that your paper is good, it is not 100% sure that your paper is ready to publish at the moment. Remember that your supervisor can see lots of other things that you cannot see in this stage.

So the bottom-line is that, try to further work on your idea and convince your supervisor that the paper is good and he -as a normal humankind- should be more than happy to co-author the paper with you since publication is one of the main KPIs for academicians across the globe.