What is the reason that only organisms belong to same species can produce a viable and reproductively healthy offspring but organisms of two different species cannot?
In sexually reproducing organisms, fusion of gametes starts of the process of embryonic development. If union of gametes between two genetically distinct species takes place, there may be two situations -
- Same number of chromosomes - Though the number of chromosomes are same, during the first mitosis, their centromeres may not be arranged in the same plane. As a result, cell division cycle arrest occurs, halting further development.
- Different number of chromosomes - The extra chromosomes which are not paired lead to differential tension on the microtubules which again disrupts the cell division cycle.
Description of cell division cycle.
The short answer is that "different species" are defined as "not being able to produce viable offspring". So the answer to your question is that it's a tautology; it's that way because that's how it's defined. You're asking a question about words, not about biology. If you were able to persuade people that a "species" was "anything living in the same area", then "different species" would be perfectly able to reproduce.
More specifically, there are many different definitions of "species", and you're asking a question about one particular definition, the "biological species" concept that was first presented by Ernst Mayr in 1942 in his book Systematics and the Origin of Species. Mayr's definition is a useful one, but it's far from the only one; there are literally dozens of other definitions of "species". See Wikipedia's The Species Problem for more information.
Still, it's worth asking why there biology does (to some extent) have "species" that don't interbreed; Mayr's definition has stuck because it is useful. The first thing to consider is how remarkable it is that any two individuals (of the same species) can interbreed at all. It's not the default option! There are thousands of highly specialized quirks that allow fertilization to happen at all. Males and females have to be incredibly fine-tuned to recognize each other, to have sperm and egg meet each other, to have the sperm identify the egg, to enter and mix genetic material ... the cascade is tremendously unlikely and has to be rigorously maintained.
So when it's not maintained -- when there's no selection pressure on two populations -- inevitably there will be genetic drift that will randomly disrupt this fine-tuned system. If a population of, say, voles is isolated on an island, they will continue to have pressure to be able to interbreed with other voles on the island, but if they can't interbreed with those on the mainland there won't be any consequences, and so over long enough time they'll drift and lose that ability -- just as many apes, not suffering any consequences from not synthesizing vitamin C, gradually lost that ability from random drift.
There's another side to it. Two populations in the same location may be positively selected to not be able to interbreed. Think about two groups of finches, one with small fine beaks that eat tiny seeds deep inside pine cones, and one with heavy beaks that crush and eat thick-shelled nuts. They each do fine, but they can interbreed and produce offspring that have intermediate beaks -- too thick to reach the fine seeds that one parent eats, but too delicate to crush the nuts that the other parent eats. Those intermediate offspring will die off, and both parents will have wasted their resources raising them. Both parents would be better off not breeding with each other, but only breeding with their own kind to produce specialized and efficient offspring. There is now selection pressure on the birds to recognize their own kind (perhaps through songs or mating displays) and ultimately to be inter-sterile, so they never waste resources on the un-fit offspring. There's a gradation of separation over time, in which the different populations become more and more distinct. Eventually, at some arbitrary point, humans start calling them "species", but that's just us, not biology.
"Species" is an important concept, but it's not special in evolution; speciation is just one aspect of natural selection, there's nothing magical about it.