You can find information about open access publishing in various online places such as the wikipedia article linked here.
Note the section on funding, however. Since readers of open access materials can do so without charge, the costs must be covered by other means. Often this means that the authors are charged a fee for publishing.
Perhaps your advisor is objecting to the cost of publication. But perhaps he is confusing it with predatory journals that also usually charge authors for publishing. The difference is that open access journals are often completely reputable (as are the ones you list), but predatory journals are not.
I believe that some reputable journals will publish either with or without the open access option. You can then avoid the fees (perhaps), but readers will need to subscribe or otherwise pay the publishers for access.
However, even without open access, most university libraries can obtain access to scholarly materials through sharing arrangements, so researchers can get access without fee. And when a journal is published by a scholarly society, the articles may be accessible to members for reduced (or no) fees.