You read it wrong. I will include all of it for context, and add commentary. Third paragraph is relevant.

I swear by [Apollo](https://en.wikipedia.org/wiki/Apollo Healer, by Asclepius, by Hygieia, by Panacea, and by all the gods and goddesses, making them my witnesses, that I will carry out, according to my ability and judgment, this oath and this indenture.

Religious mumbo jumbo but standard for its time

To hold my teacher in this art equal to my own parents; to make him partner in my livelihood; when he is in need of money to share mine with him; to consider his family as my own brothers, and to teach them this art, if they want to learn it, without fee or indenture; to impart precept, oral instruction, and all other instruction to my own sons, the sons of my teacher, and to indentured pupils who have taken the Healer’s oath, but to nobody else.

Medical knowledge should be free! You hear that, America?
Also, no “First do no harm”, it’s “first, respect your teacher”.

I will use those dietary regimens which will benefit my patients according to my greatest ability and judgment, and I will do no harm or injustice to them.[6] Neither will I administer a poison to anybody when asked to do so, nor will I suggest such a course. Similarly I will not give to a woman a pessary to cause abortion. But I will keep pure and holy both my life and my art. I will not use the knife, not even, verily, on sufferers from stone, but I will give place to such as are craftsmen therein.

See, no doctors with knife! You can get another “craftsman” to operate on you but better make sure he is the son of a doctor, because all others have never received medical training (see end of second paragraph) or taken this no-knife oath.

Into whatsoever houses I enter, I will enter to help the sick, and I will abstain from all intentional wrong-doing and harm, especially from abusing the bodies of man or woman, bond or free. And whatsoever I shall see or hear in the course of my profession, as well as outside my profession in my intercourse with men, if it be what should not be published abroad, I will never divulge, holding such things to be holy secrets.

Do no harm, also don’t rape and keep secrets. All good…
Wait! "outside my profession in my intercourse with men”
Hippocrates is gay, confirmed

Now if I carry out this oath, and break it not, may I gain for ever reputation among all men for my life and for my art; but if I break it and forswear myself, may the opposite befall me.[5]
– Translation by W.H.S. Jones.