I just read that according to the BBT the universe is expanding. This is evident from the fact that distant stars (and galaxies) are moving away from us. But it could also happen that the universe is in fact shrinking to a very small point and we being far away from the point are experiencing its pull less than those that are near it. It may be like a race where a very fast (in 1st place) , a moderately fast (in 2nd place) and a slow car (at last) are racing . To the moderately fast car it would seem that the other two are moving away from it,but actually they all are moving towards the same point -the end. So it may happen that earth is like the moderately fast car moving towards the collapse point at a different relative speed. Is this proposition possible? If not,why?
Galaxies are moving away from us in every direction.
If it were like your race, galaxies at our same distance from the central point will be slowly approximating. That is, we will note that galaxies nearer to the center than us will move away from us (since they are faster), galaxies in the opposite side of the sky will move away from us (since they are slower), and galaxies in the plane that lies between these two point will be slowly approximating to us (since we converge with them to the same point at the same speed).
So the answer is no, that is not a possibility.
As has been pointed out the expansion of the galaxies is seen in all directions. But there is other evidence to support theory of cosmic expansion - such as the red shift in the cosmic microwave background (CMB). The CMB is the radiation left over from a specific event - the moment when the primeval fireball's temperature dropped sufficiently to allow the stable recombination of electrons and protons into hydrogen atoms.
That happened when the universe's temperature (and remember this was a relatively smooth plasma so this happened more or less everywhere at the same time) fell to about 4000K
But the CMB we see today has been so redshifted that the CMB looks like the signature of an event that took place at a temperature of about 3K - the reason is that the universe has expanded by so much (in all directions) that the radiation from the CMB has been "stretched" into these much longer wavelengths on its journey to us.