Why do charges result on atoms when coordinate bonds are formed?
The first thing to note about the charges that form during the formation of a coordinate bond: They are a formality.

The second thing to note about the charges that form during the formation of a coordinate bond: They are a mere formality.

There is little correlation, if any at all, between the formal charges assigned to two atoms that have formed a coordinative bond and the actual charges observed in the compound. Take $\ce{H3N-BH3}$: Nitrogen is so much more electronegative than boron, that the electrons are still closer to the nitrogen. Thus, nitrogen has $\delta ^-$ while boron has $\delta ^+$.

So where does the formalism come from? When drawing Lewis structures, after having filled in all bonds and lone pairs, check every single atom and mentally cleave all its bonds homolytically. Count the electrons, subtract the amount it should have as a neutral atom and the difference is its formal charge. Boron would have four electrons if all four bonds be cleaved homolytically, but it should only have three, so it gets a $1-$ charge.

This is only a formalism so that you can basically derive all structures the same way. It has no physical significance.



There are enough people who were unhappy about the ‘wrong’ charge distributions that they proposed different methods to draw these compounds: some used arrows from donor to acceptor, others just drew a simple bond, knowing that it would be different from a covalent bond. Each method has its advantages and disadvantages and all have survived in at least one niche.