Confusion about Titration Formula
Your title and the main body of the post are two different questions. Anyway, it is important to understand the difference in each case.

Let us talk about the analyte. Your analyte can come in two forms: (i) either as a solid or (ii) as a solution.

In the case of a solid analyte you would quantitatively transfer a known exact weight of the sample to a flask, let us say an Erlenmeyer flask. You can now add some water to dissolve it and you do not need to worry because you have recorded the actual weight of the sample. [yes the conc. will change, depending on how much water you are adding].

In the case of a analyte solution you would quantitatively transfer a known volume with the help of a pipette to an Erlenmeyer flask. You can still add some water and need not worry because you know the initial volume.
[again the conc. will change with the addition of water].

*What is important in titration calculations are absolute moles of the analyte not its total volume in which it is being titrated*. 

Now why can't we add water to a buret? The reason is that by adding water to buret, it will change the concentration of the titrant. As I said earlier, only moles are important in the calculations, and moles of titrant can only be calculated by

[Volume of titrant][Conc. of titrant] = moles of titrant

if the [Conc. of titrant] is an incorrect number, which has changed by adding water, the moles of titrant will be a wrong number.

Eventually, we calculate the concentrations with the initial volume we added with the help of pipette or a known mass.

*The problem is arising because you are using a titration formula taught by those who shouldn't be teaching science. This formula is not only wrong (prone to error), but it will lead to all type of problems in future with redox calculations. I strongly discourage using the formulae given in your query.

[Acid] = (Volume of Base)*[Base] / (Volume of Acid)

This formula is valid for all acid-base and redox titrations iff (if and only if) concentrations are provided in normality. Normality is an ancient 18th century concept. It has stuck in certain education systems like cancer. You quash it here but it appears somewhere else.*