Should you revise a manuscript when only two of the three reviewers provide a positive review?
To add to the other answer that has been posted so far (from @mgbdog), I will add something from the perspective of a past editor in chief and frequent associate editor, in the field of computer science.

Generally (look at the various posts about journal workflows) the reviewers provide their feedback, an associate editor recommends, and then the editor in chief either accepts that recommendation or pushes back in some fashion.  So the comment about the editor wanting to proceed is accurate in the aggregate but it really refers to multiple people as a rule.

But the key here is that when one reviewer recommends rejection, and other reviewers were more positive, I assume that the OP received a "major" revision that means it will be returned to the reviewers.  Two already liked it so probably will be in favor of the revision.  The one who didn't, if they were negative enough, may actually not be willing to review it again (after all, the editors didn't listen to them).  I have encountered that several times as an associate editor.  If they do review it again, hopefully they are professional about it and read it with an open mind, and you get your opportunity to improve the paper and respond to their criticism.  So hopefully they are convinced to accept.  

If they don't, there is indeed a chance the paper will be rejected after revision.  Just because the editor said to give you a chance to fix it doesn't mean in the end it is fixable.  I once did a journal article that got back extensive comments and a very specific warning from the associate editor that we should not assume that the major revision we were doing actually would result in acceptance. We must have worked on it for another year and with a second minor revision after that, but it got in.  

But just because it may be rejected doesn't mean you shouldn't try.  With 2/3 favorable, you seem well positioned, as long as you believe you can either fix what #3 complained about or make an argument in your response that they have it wrong.