The reality is that you should not reuse motor oil that you have drained out of your engine. Engine oil protects your engine by keeping contact surfaces lubricated. Proper lubrication relies on oil being extremely clean and free of contaminants. When you buy oil new and pour it out of the bottle for the first time, it is completely clean and free to debris. Once you drain it into an oil catch pan, you no longer have the guarantee that there is no foreign material in your oil.
Even particles that are small enough to be almost invisible to the human eye are enough to do significant damage to your engine if they end up in the wrong spot. Small, hard particulate can easily score bearings, damage pumps, or obstruct small oil pathways in certain internal engine components. Even doing a wipe down with a good shop towel for anything used to hold the oil with isn’t always enough to protect yourself from the possibility that foreign material makes it back into your engine if you reuse your oil in this fashion, because it’s simply too easy to miss small debris.
When you start to compare the cost of potentially expensive engine damage that could occur if you choose to reuse your oil against the relatively inexpensive cost of replacing your oil, the risk just isn’t worth the reward. This is especially true as the oil you removed presumably isn’t brand new, which means you have likely already gotten some miles out of it and thus have extracted some of its value already. The same logic applies regardless of whether your car uses synthetic motor oil or conventional motor oil.
In the end, putting new oil in your vehicle after you have drained your motor for a repair is the safe and smart way to go. You should view it as cheap insurance against possible catastrophic engine damage due to possible contaminants your used oil could pick up while temporarily outside your engine.