The answer probably lies in how legs are form, that is from segments. Most animals come from a basic design that consists of segments with one pair of limbs per segment (think of a centipede), this basic design goes right back and is fundamental to vertebrates and so you only really get pairs of legs hence you don't get three.

To look for odd numbers you have to go to the inverts and here it comes down to symmetry and segmentation. For example many starfish have five arms but they are radial symmetrical rather than bilaterally symmetrical and so they body segments are arranged around a central axis not a longitudinal axis. Five is a neat number as it ensures you don't have any obvious points of division - that is why older cars have five wheel nuts on each wheel - to ensure that opposite each nut is solid wheel and not another nut so there is less chance of a fracture line going through two or more nuts. So you can get odd numbers of legs but only in radial symmetrical organisms and most of those are invertebrates. Maybe three is too few legs to be useful in a radial design.

An animal, if ever had three legs, would find difficulty to balance itself while changing its position (moving), that is why God created all the living oranisms with either no legs (snake), or two legs(human) or four legs (horse, dog etc).

It isn't true that there are no animals with an odd number of legs - starfish have five. At least, they really walk on lots of little tube feet, but the tube feet are arranged in groups underneath the five visible limbs.

Three limbs might actually work for something like a starfish which is basically lying down, but three is an unstable number for any animal which stands up off the floor, because as soon as it lifts one foot to go forwards it is standing on two limbs, and may topple.

Advanced quadrupeds such as dogs and cats can manage very well on three legs, because they have a good sense of balance and because their feet naturally fall close to the midline of their centre of gravity. Even though as soon as they raise a paw they are left teetering on two limbs, they only have to sway very slightly to get their weight balanced over the remaining two feet - and in fact at a fast gait quadrupeds often pick two feet off the floor anyway and balance on the other two.

Then there are bipeds such as humans or birds, who go on two feet all the time, and have to balance on one foot as they step forwards with the other. But again, such bipeds have a good sense of balance and their feet positioned well under their centre of gravity; and they evolved from quadrupeds.

However, animals which were first developing the ability to walk on land - amphibians, early arthropods etc. - tended to be low-slung with their feet placed well out to the side, and they were only just learning to balance on legs. A three-legged crab or newt would either fall over as soon as it lifted one foot off the floor, or have to sway violently to get its weight over the remaining two feet, thus wasting energy.

So emergent walkers needed four or more limbs. All land-walkers seem to have gone for an even number of limbs arranged in pairs, probably because developmentally-speaking it's nice and easy to code for one pair of legs on one body-segment, and then just repeat the same bit of code as many times as you need it. And if you've got a string of legs down either side, then your other body parts get arranged to fit, with a mouth at one end and an anus or cloaca at the other.

Re-shaping themselves to have only three limbs would thereafter be very difficult, since their body had adapted to hang its organs in the gulley between two rows of limbs, and there would be no clear evolutionary benefit to evolving from a multi-paired to a three-limbed form. There's probably nothing that three legs could do that couldn't be done better by either four or two, since a triped would have neither the fast simple gait of a biped, nor the stability of a quadruped.

The only way I could see that you would get a three-legged walker would be if you started with a thick-tailed biped such as a kangaroo, and the tail then gradually evolved into a sort of extra limb. Aquatic animals, for whom falling over isn't an issue, do sometimes end up effectively with three limbs. Whales and dolphins, for example, use their flippers and tail as their three swimming limbs and so do many fish (although some also use their pelvic or dorsal fins as well). There are some fish which actually walk on the sea-bed using their pectoral fins and tail as a tripod - although those who emerge and do so on land are unable to walk with three limbs without falling over, and either progress in awkward hops or lie on their bellies and row, so that they have nowhere further to fall.

If you are going to count starfish "arms" in the leg debate...

What about tripod fish (search for them for pics/vids)? Okay so they are modified fins and they mostly just stand on them but there are definitely 3. Give then a few million years more and we may even get there.

Just as a matter of interest, flies which have six legs walk by moving three legs at at time.  This means that have always a stable footing, a tripod being extremely stable even on an uneven surface, but produces the characteristic zig-zag movement observed.