Well, it's generally not necessary to save all of the old water. But there may actually be a case where one would need to do this. For example, if your tap water has 0
nitrate and a
pH that is very different from the pH of your tank water (and I assume your tap water has 0
ammonia and 0
nitrite), then it would be rather dangerous to dump all of the old water and fill the tank with 100% new tap water. This is because the fish may get a pH and/or a nitrate shock. Suppose your tank nitrate is 30 and pH is 7.5, and that your tap nitrate is 0 and pH is 6.5 - in this situation, when your fish suddenly go from your tank water to a whole tank of 100% new tap water, they could experience a pH and/or a nitrate shock. When I was transferring my 30 gallon tank, I actually saved some 80 - 90% of my tank water in buckets. I put the fish in a bucket with tank water and I hung the filter on another bucket with tank water (and kept it running). Then, I emptied my tank and transferred it to another room. Next, I put all the saved water back in, put all the fish back in, added the 10 - 20% of new water, and hung the filter on the tank and let it run on. The whole transfer must have felt rather like a water change for fish, because I didn't change 100% of the water, but only 10 - 20%. Nothing bad happened to fish afterwards. All was well.
This is a good way to do this if your tap and tank pH and nitrate are very different. If they're not, you probably wouldn't have to save 100% of the old water. You could save only enough for the filter to run and for the fish to swim in, while you're transferring the tank. However, if your tank is large and the tap and tank pH and nitrate are very different, try to save at least 50% of old water. Always remember to keep the filter running on the bucket with tank water during the time when you're transferring a tank - this way the beneficial bacteria will not die off.