Sometimes different species mate and they are able to have offsprings, usually with anomalies. Are there known requirements for 2 different species to produce offsprings? Why species like the lion and the tiger, which seems to have many differences are able to produce offsprings, when others which supposedly share 99% of the DNA can't?
Lets break this down like a logical problem. In reality, it involves the correct gene expressions at the correct time, place, etc. But that would be a book.
Prezygotic reproductive isolating mechanisms
A bull and a whale can't mate; they don't live in the same environment. Lions and tigers similarly do not mate in the wild due to lack of overlap in the environment. In captivity, yes.
Delivery of gametes
Sperm must be able to be delivered to the ovum for fertilization to occur. Some species just can't get this part right. Your house cat would not be a suitable donor for an elephant.* In closer species, say a chicken and a peacock, the rooster's courtship display (which is nowhere near as spectacular at the peacock's) will not be accepted by the female; no opportunity for delivery of gametes.
Some gametes can be delivered but not ova (the female isn't "in season".) Zero there as well.
Unity of gametes
If the gametes are both delivered at the correct time, can the sperm bind to the egg? Successful binding requires a receptor-ligand interaction which actually has a high degree of species specificity. So binding requires that the sperm and the egg can, say, "communicate" successfully. Dog sperm doesn't "speak" cat ovum.
If they do "speak the same language", can the sperm penetrate the ovum's protective coating (the zona pellucida)? Assuming sperm capacitation (a big hurdle right there), the sperm may not have the correct enzymes in it's 'head' to penetrate zona pellucida. Not all enzymes carry out the same function on all molecules, and if the correct enzymes are present to digest/break through the zona pellucida, is there enough? Is the sperm active enough? I'll liken this kind of communication to 'pillow talk'. We're getting much closer. Let's say the sperm has his pillow talk down, and can penetrate the layer.
Postzygotic isolating mechanisms
The hybrid embryo must be able to develop into a zygote. Hybrid inviability means there wasn't enough similarity to proceed to a blastocyst and the hybrid dies.
Say viability is achievable. The blastocyst/blastomere must "communicate" with the mother so that attachment is not only possible but can be sustained. In effect, it must "shout" to the mom, "I'm here! Pay attention to me!" (In humans, this involves secretion of large quantities of a hormone called chorionic gonadotropin, which stimulates continued secretion of progesterone, thus no shedding of the uterine lining. Not all mammalian blastocysts communicate the same way. If what we have here is a failure to communicate... as with Cool Hand Luke, the result is not good.
The species were close enough for the conceptus to be heard by the mom. The right chromosomes with the right gene expression results in a live birth.
If the hybrid is fertile, it is by one definition not a different species. (There is much debate as to what exactly defines a species. See the references.)
If you are still left saying, "But why?", then it must be explained on a genetic/molecular level, with sentences like,
The zona pellucida of mammalian eggs is composed mainly of three glycoproteins, all of which are produced exclusively by the growing oocyte. Two of them, ZP2 and ZP3, assemble into long filaments, while the other, ZP1, cross-links the filaments into a three-dimensional network. The protein ZP3 is crucial: female mice with an inactivated ZP3 gene produce eggs lacking a zona and are infertile.
If this is the level of explanation you seek, there's a book for you: Molecular Biology of the Cell. Alberts B, Johnson A, Lewis J, et al.
*Note here I'm referring to morphological differences, one way used to define species.