The people who claim Francis Crick believed life did not arise on earth need to provide a definite source for that assertion. I looked and couldn't find one. They should probably modify their assertion to say that Crick once believed it was so unlikely that life arose naturally on earth that he conducted his own theoretical investigation into the possibility of directed panspermia and concluded there was no reason to believe in an earthly origin rather than an extraterrestrial origin of life.
In
Life Itself by Francis Crick he says,
An honest man, armed with all the knowledge available to us now, could only state that in some sense, the origin of life appears at the moment to be almost a miracle, so many are the conditions which would have had to have been satisfied to get it going. But this should not be taken to imply that there are good reasons to believe that it could not have started on the earth by a perfectly reasonable sequence of fairly ordinary chemical reactions. The plain fact is that the time available was too long, the many microenvironments on the earth's surface too diverse, the various chemical possibilities too numerous and our own knowledge and imagination too feeble to allow us to be able to unravel exactly how it might or might not have happened such a long time ago, especially as we have no experimental evidence from that era to check our ideas against. Perhaps in the future we may know enough to make a considered guess, but at the present time we can only say that we cannot decide whether the origin of life on earth was an extremely unlikely event or almost a certainty—or any possibility in between these two extremes.
However if you look at Crick's argument he is saying it is unlikely that life evolved on earth but maybe there is something we don't know about that could explain it.
Science is not about "maybe there is something we don't know". When everything you know about science tells you something didn't happen, the rational scientific assessment is that the best interpretation of the evidence is that it didn't happen. Anyone is free to propose all the hypotheses they want but an untested hypotheses does not contradict the current state of scientific knowledge. People, even scientists are not very rational, we prefer to believe what pleases us and invent mysteries to satisfy our psychological needs.
https://profiles.nlm.nih.gov/ps/access/SCBCCP.pdf
Directed Panspermia
F. H. C. CRICK
Medical Research Council, Laboratory of Molecular Biology, Hills Road, Cambridge, En,gland
AND
L. E. ORGEL
The Salk Institute for Biological Studies, P.O. Box 1809, San Diego, California 92112
Received June 22, 1972; revised December 20, 1972
...
Thus the idea of Directed Panspermia cannot at the moment be rejected by any simple argument. It is radically different from the idea that life started here ab inito without infection from elsewhere. We have thus two sharply different theories of the origin of life on Earth. Can we choose between them?
At the moment it seems that the experimental evidence is too feeble to make this discrimination.