Why is gravity only an attractive force? As per the universal law of attraction, any two bodies (having some mass) experience a force of 'attraction' which is proportionate to ...and ...inverse proportionate ....

Then comes my question: Why it should be force should be of type 'attraction' only ?  Why it should not be repulsion / any other kind of force ?
Because mass is positive

To expand your quote concerning the gravitational force into an equation:

$$F_G = -\frac{Gm_1m_2}{r^2}$$

The force of gravity, $F_G$ is proportional to the product of the masses and inversely proportional to the distance, $r$, squared. Let's break this down and see what might cause $F_G$ to be positive.

In this equation, $r$ cannot be negative because it's a distance between two locations. Two locations cannot be a negative distance apart. And even if they somehow were, the squared would take care of that anyway.

$G$ is the universal constant and always positive. You might argue that it could possibly be negative, but that's not possible. $G$ actually doesn't really exist. It doesn't describe anything fundamental to the physics of the universe. $G$ is simply a bookkeeping constant that allows us to get the right answer for the force based on any choice of units for mass and distance. Technically, if one uses the "correct" units for mass and distance (e.g., the Planck units), then $G=1$ and effectively doesn't exist. Since $G$ is just a scaling factor that depends on the choice of units, it will only be a positive number.

That leaves us with the masses. These are the only things which could possibly be negative. Of course, to get a positive, repulsive force, one mass would have to be positive and the other negative. But what exactly is a negative mass? Mass is the metric which describes "how much" of something there is. How can you have less than nothing of something?

Why can mass not be negative?

If you want to look at this another way, you can show that if mass could be negative, you'd get nonsensical results! Assuming of course, all other aspects of physics were the same. Recall from Newton's second law that

$$F = ma$$

Let's say there are two blocks sitting on a table. One block has a mass $m_1&gt;0$ which is positive and the other has a mass $m_2&lt;0$ which is negative. Ignore all other forces on these two blocks for the moment.

I go up to $m_1$ and I apply a force to push this mass forward. The acceleration that is induced is: $a = F/m_1$. Necessarily, the direction in which $m_1$ moves is the same direction in which I'm pushing. That's all well and good.

Now I go over to $m_2$ and I apply the same force, attempting to push it forward on the table. The acceleration induced on $m_2$ will be: $a = -F/|m_2|$. Note I made $m_2$ positive and pulled out the negative sign. You can see that if my force is forward, the direction the mass moves will be backwards! But here's the problem, my hand is in the way because it's trying to push to mass. As the mass tries to move backwards into my hand, it will be applying a force back on my hand, which by Newton's third law, necessarily mean's my hand is applying more force on the block, which then applies more force on my hand, ... and suddenly infinite forces are being applied or equivalently, these objects are infinitely accelerating. This is described by the concept of Runaway Motion.

If this seems strange to you, that's because it is. If negative masses existed, we'd live in a very weird universe. Fortunately, we live in a universe where physics makes sense, mass is positive, and by extension gravity is always attractive.