How come when you have recessive and recessive, there is a probability of a dominant gene coming out?

...do you mean if you mix an rr with a dominant there is a chance that it will come out dominant? because there is... rr cross with Rr... posibilities... Rr, Rr, rr, rr

Well brother the rr genes are recessive because when dominant genes are expressed they are supressed. So in a cross of rr with rr there are no dominants hence it doesnt matter whether you call them recessive or dominant because they will always be expressed.

If we see both alleles r and r are recessive it has to do with the expression of genes which is controlled by many factors in the cell, including gene regulation and expression.

All dominant means in genetics is the expression.  There are two types of dominant genes biochemically speaking.  The first is a 'dominant negative', where a gene becomes mutated and somehow blocks the good genes.  If this is the case only one mutation is enough to remove the function of both copies of the gene (the dominant negative copy and the wild-type copy).  This is teh case in p53, where the DNA binding domain is mutant, but the tetramerization domain is intact.  So this protein will bind to normal p53 protein, and inhibit DNA binding of teh complex. The second type of dominant gene is one that give a phenotype.  For example, a gene to give a flower red color may be dominant to white.  This can be a novel activating mutation or something else.  

So in your example if there is no dominant R allele, the 'r' allele would be expressing.  Maybe that is what your teacher meant; i would ask him/her to clarify the issue.