Why can't we reach to Speed of light at Space?

[phinds]

. Then we turn around and say mass increases with velocity.

I don't have any idea who that "we" is that you are talking about. I'm not aware of any knowledgeable physicists who says any such thing and you will not find any such members of this forum saying so. There are HUNDREDS of threads on this forum pointing out that objects do NOT gain mass in that manner, they gain energy.

 

[Neandethal00]

Since energy and mass are equivalent in relativity, the object's greater energy can be considered as greater mass.

Good, this can be one interpretation of effects of velocity on special relativity.
My thinking is it is not mass that increases, it is the inertia that increases requiring larger energy to move through space.
We know very little about interaction between 'empty space' and matter.

If there are 'fish scientists' in the ocean, the fish scientists formulate theories of physics to explain everything to other 'fish' totally ignoring the 'water'.
That's what we (Yes, Phind, I consider myself a scientist, it is called self criticism) are doing now.

 

[PWiz]

there are 'fish scientists' in the ocean, the fish scientists formulate theories of physics to explain everything to other 'fish' totally ignoring the 'water'.

We do that with light because there is no "medium" required for it to propagate through - no "ether". This might not always be the case with other phenomenona.

My thinking is it is not mass that increases, it is the inertia that increases requiring larger energy to move through space.

That's right. This is best demonstrated using a force 4-vector: $F_μ = γ\frac{∂p_μ}{∂t}$. This implies that the force required to accelerate an object at a constant value tends to infinity over time (for rectilinear motion).