Why Commonsense expressed in Logic is a bad idea

Why Commonsense expressed in Logic is a bad idea - 

Suppose I say to you - 

X > X - 5        since anything will be greater than something removed from it. This is commonsense thinking. The basis of the proposition here is commonsense.

Now, one might argue that - 

Logically, 

0 > -5

add X to both sides,

so, X + 0 > X -5

so, X > X - 5

Hence, the same thing can be arrived at and represented logically. 

But logic doesn't capture the reasoning process / the rationale in the above instance of commonsense thinking - that anything will be greater than something removed from it. This is fundamentally different from the logical process of deduction shown above. It (the former) comes from human experience of reality - all that we have experienced about 'amounts' in our lives, till the point of putting forward that propositional basis. But all that can be challenged logically by saying that - all this (experience) is finite and only up-till now; how do you know about other cases and the future ? Also you don't have a record of all the instances of dealing with amounts in your life; may be some skipped from memory. Still, that commonsense thinking piece remains the strongest perceptual force we have of being sure about what we are doing. Putting another way, just imagine how strange it would be if someone doubts that reasoning and believes only in the logical deduction shown above. That would amount to no sense of real understanding / cognition.