The issue arises due to evolving definitions over time and in particular the use of professional as an 'opposite' of amateur which is flawed.
If you begin with a definition of Profession
"
A Profession is a disciplined group of individuals who adhere to ethical standards and who hold themselves out as, and are accepted by the public as possessing special knowledge and skills in a widely recognised body of learning derived from research, education and training at a high level, and who are prepared to apply this knowledge and exercise these skills in the interest of others.
It is inherent in the definition of a Profession that a code of ethics governs the activities of each Profession. Such codes require behaviour and practice beyond the personal moral obligations of an individual. They define and demand high standards of behaviour in respect to the services provided to the public and in dealing with professional colleagues. Often these codes are enforced by the Profession and are acknowledged and accepted by the community".
A Professional is a member of a recognised profession based on the above definition. This will include the fields of healthcare, law, teaching etc. In most instances professionals will receive remuneration for their activity, but it is not strictly part of the definition.
The definition of 'amateur' is a little more straightforward, ie someone who carries out an activity for no remuneration and where others may carry out exactly the same activity for payment.
Usage of professional to compare to 'an amateur' to distinguish between someone who is paid or not, has become widespread and has especially been driven by sport.
This is deemed acceptable usage, but is not strictly accurate as professional refers to the way in which members of a profession have gained knowledge and in how they behave and are governed etc as in the above definition, rather than whether they are paid or not.
Consequently many members of professions may offer their services for free (this is common with eg voluntary work) and many amateurs may still strive to carry out an unpaid activity in a 'professional' manner.
The English language ... don't you just love it
Just to add that prostitution is often described as 'the oldest profession' which is also seriously flawed
