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Penrose did not "discover" black holes. Granted, he did a lot of work on the theory of black holes, and coined (I think) the term, but he did not discover any black holes. In fact, there still has not been a black hole discovered. There have been several things observed, which fit the theory of black holes, but there is no conclusive evidence.

My mistake, Penrose did not "discover" black holes. He, along with Hawking, proved that if General Relativity is true, then black holes are inevitable.

Here's a thought puzzle for you. Suppose that Penrose and Darwin were alive at the same time. Suppose further that Darwin claimed that black holes were impossible, because they were too unlikely. Would you then say that Penrose was wrong, because Darwin said so? After all, Darwin "discovered" evolution.

Well, obviously one of them is wrong, because Penrose showed that black holes are inevitable in General Relativity. Darwin would have to have committed a blunder.

I suspect that if you were to poll physicists and biologists, you would find more physicists that don't believe in black holes than biologists who don't believe in evolution.

Surely you are joking. Lets bet: I will buy you and a companion dinner in the NYC restaurant of your choice if you can show me one article in a peer reviewed physics journal wherein the author presents an argument that block holes do not exist. If you formally accept within the next 24 hours and fail to provide the evidence within 7*24 hours then you must buy me and a companion each a Krispy Kreme donut in the NYC Krispy Kreme stand of my choice.

Quotes and references:

Direct observational evidence for the existence of black holes has not yet been discovered. However there is some indirect evidence such as Cygnus X-1, where a black hole is one of the most feasible explanations of the available observations. General Relativity seems to demand the existence of black holes. The work of pioneers such as Chandrasekhar, Oppenheimer & Snider in establishing the existence of an upper limit to the mass of any kind of star lends strong support to the concept of black holes, while Hawking and Penrose have shown that singularities are an inevitable consequence of general relativity.

In the last decennia there has been lots of improvement in the research of SBH's, the current models are as fully functional as they could be, only the accuracy can always be higher. The measured data can't fit the models if there isn't a SBH in the center of the galaxies, therefore the must be there. Older models (which require less computer capacity) sometimes cannot rule out multiple smaller dark objects but newer models can mostly. These newer models and better telescopes also show new candidates for SBH's which need to be further examined. The spatial resolution of the data can still be improved so we can find SBH's with even more accuracy. Some of the current research show probabilities of SBH's even over 99.9%, so there must be a SBH in the center of some of these galaxies. This proves that there has to be SBH's, therefore that Black Holes exist in general.

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