Alternatively, you can keep the Filter panel open on the right and turn the "text is 'false'" filter on and off. The advantage to using the filter panel is it makes it easier to add new rows. It appears you cannot add rows to your table when a filter is on.
Another alternative, would be something like this:
Formula in B2 = AND(C$1,C2)
Fill down to complete column
The filter for column B is "Show rows containing FALSE". Or, if using the Filter panel on the right, the filter for column B is "Text is FALSE". After it is set up, hide column B
When the checkbox in C1 is checked, any row with a checked box will be hidden. When unchecked, all rows will be shown. You could put that checkbox in another table. That table would have only two cells, one cell to write "Click here to hide rows", the other being the checkbox.
If you would rather the checkbox be checked to show all rows, change the B2 formula to =AND(NOT(C$1),C2). Now the rows will be hidden when the box is unchecked and will display when the box is checked.