In your question, your assumption that animal species are less diverse phenotypically than humans is wrong. I am sure you will appreciate @terdon's answer to this post and @GriffinEvo's answer to this post.
Don't forget that we are good at detecting differences among humans (because we evolved for this purpose). We are doing much worse at telling apart animals from other species just because we have not evolved for this purpose. This is the reason why we tend to see human faces when looking at clouds but we rarely see sheep faces! Several studies (here and here) showed that sheeps are able to recognize each other (and we even know the number of neurones needed to remember one face). They are probably better at telling two sheeps apart than telling two human apart.
Another interesting fact is the so-called cross-race effect. We, humans, are better at recognizing faces of people from our own ethnic group than faces of people from other ethnic groups. For example, a japanese is very good at japanese faces recognition but not good at recognizing european faces. Same is true the other way around.
As @user568459 said in the comments: some people are not able to recognize faces. This is due to a cognitive disease called Prosopagnosia (also called face blindness). Those suffering from this disease are not better at recognizing sheep faces than human faces.
So consider the class of cats they are one type of species so why aren't they diverse in phenotype like us?
There is no good definition I think of what is phenotypic diversity (no accurate and objective index to measure it) but at first sight I would tend to think that cats are more diverse than humans. One of the main feature one would probably raise when talking about human diversity is skin color. And in terms of color, cats are much much more diverse than humans. You may think of an extraordinary diversity when thinking of Norvegian that are taller than Indonesian (I may not have chosen the two extremes) by several centimeters on average but think about cats! The average cat weight 4 to 5 kg but some cats weight less than 2kg and some other (like the coon cat) weight more than 10kg (World Record: 21.3kg). Imagine a human ethnic group that would on average weight 5 times more than another ethnic group! And think also about cats' hair length or tail shape! Humans vary in terms of facial feature (lips size, nose shape, etc..) so do cats. Some look like their face was smashed against a wall while others have a long muffle. Again I welcome you to have a look to this post.
how they can know each like a bird always brings food to his offspring and it can't make mistake by giving it to other offspring of it's own species?
As I said above humans evolved to recognize their own. Many species also evolved in order to recognize their own. In some species individuals use smell rather than visual features in order to recognize each other (odor is also a kind of phenotypic variation). But still some species are poor to recognize each other. For a bird, it seems rather easy to not feed the wrong individual as all their offspring are usually together in the same nest. However you might be interested the lifestyle of the cuckoo who parasites nests of other bird species. Cuckoos' babies and particularly the inner beak ressemble to the babies of the species they parasite and often the parents (often the mother only is involved in feeding the youngs) get fooled and feed the cuckoo.
So can i say they aren't diverse because of in their meiosis division their chromosomes don't cross over and random assort (alignment)?
No, you can't say that! Because they are diverse and because for many of the species of may think about, cross-over does occur. Their genetic diversity as well as their phenotypic diversity is as high than in humans. There is nothing extraordinary about humans (except their brain and the related fact that we predigest our food by cooking it) compare to other lineages. And there is nothing extraordinary to have one extraordinary feature (such as a big brain) that you can't find in other lineages! Many lineages are extraordinary in some sense.