I have tried drawn numerous tables in attempt to explain this and understand that the number of cells must be even however, I am not sure how to create this proof. I appreciate your support.
Each cell of a square table is filled out either with a plus or minus. It is known that the total number of pluses is equal to the total number of minuses. Prove that there are either two rows or two columns of the table that contain the same number of pluses.
Note that for the $n\times n$ grid, $n$ must be even, in order to satisfy the condition of an equal number of pluses and minuses
In order for all the rows to have different numbers of pluses, we'd need to have rows having $n$ of $0,1,\dots,n$ pluses. But the $n$ numbers we choose from $0,1,\dots, n$ have to add up to $\frac{n^2}{2}$ (since half the grid has pluses).
Using the well-known formula $1+2+\cdots+n=\frac{n(n+1)}{2}$, we see that the unused possible number of pluses must be $\frac{n}{2}$.
In particular there must be a row with $0$ pluses and a row with $n$ pluses.
A similar argument will hold for columns.
Now consider that a row of $0$ pluses is incompatible with a column of $n$ pluses.