Pilot reported a flight attendant was ill and went to go get a quick COVID test. Pilot reported that management attempted to force the pilot to depart against pilot's wishes.

Narrative

When we arrived at ZZZ from ZZZ1; I learned that one of the flight attendants was feeling ill and that she strongly suspected that it was COVID. The flight attendants were very professional and the sick flight attendant had no incentive to lie about it. After all; being COVID positive would prevent her from going home. Also; if she is sick from COVID; then all of the flight attendants are likely exposed.We passed on the information that a flight attendant is sick and that the others are possibly exposed. The sick flight attendant went to take a COVID test and we understood that it should take only about 15 minutes. We considered this to be the quickest and safest option. If she tested negative; then we can go with a replacement flight attendant. But until then; the flight attendants did not consider themselves to be fit to fly; and I did not consider them to be fit to fly either. Also; adding a new flight attendant to an infected crew would only get the new flight attendant infected.The process of the flight attendant getting tested was taking much longer than I expected. The Flight Manager entered the cockpit and told me that I am holding up operations. Apparently; he wanted us to go with a replacement flight attendant without checking for exposure or even making sure that the aircraft was sanitized. I told him my concerns about crew exposure and aircraft contamination. I even pointed out the possibility that I might be exposed. He said that I shouldn't be exposed; and I gladly conceded that point. I was glad because it meant that I could go home after the remaining 2 flights (even if I had to do so the next day) without being stuck in quarantine. However; in the absence of testing; I wanted to make sure certain areas of the aircraft were sanitized and that I had a new crew. This is because I considered the aircraft to be potentially contaminated and the flight attendants (although professional) to be unfit to fly. The flight attendants shared the same opinion about themselves.We disagreed on the need for sanitization. He expressed the belief that the coronavirus does not linger on surfaces. This belief grossly contradicts scientific literature which explains that the coronavirus can linger on smooth surfaces for up to 3 days. During the discussion; he mentioned that I could be making career decisions here. I then calmly asked if my career was being threatened. He said no. But his statement about career decisions can only be interpreted as a thinly veiled threat against my career.As the Captain; I said that I wanted to make sure that some areas were sanitized. I would have gladly accepted any type of action that could be interpreted as sanitization or reassurance thereof. But the Flight Manager flatly said no without giving any explanation. This is essentially saying that he will not allow me to receive these services regardless of their availability. This is a direct attack on my authority as the Captain.As the Captain; I also asked for new flight attendants because I considered them to be unfit to fly (due to their circumstances). The Flight Manager flatly said no without giving any explanation. This prevented me from getting a new crew regardless of their availability. This is another direct attack on my authority as a Captain.The Flight Manager then pressed me on answering if I will accept the flight. From my standpoint as the Captain; that is asking me if I am willing to fly a potentially contaminated aircraft with an unfit crew. I said no. The Flight Manager retaliated by giving me a Missed Assignment. At this point; it became a clear case of Pilot Pushing enforced with retribution.Potential COVID exposure; Management wanting to launch a flight without proper safety precautions; Flight Manager trying to override the Captain's authority; Pilot pushing enforced by retaliationDo not try to override the Captain's authority; especially when the Captain has a safety concern.