The fact that you can't answer this strongly suggests you don't know why you're writing estimates (or at least that you disagree with your colleague why you're writing estimates). This is a bigger problem than whether the estimates should or shouldn't include testing.
Find out, or reach agreement, why you're writing estimates. If it's to predict what a particular team will achieve in a particular time, then the answer simply depends on whether that team, the one you're estimating for, does the testing or not. If your QA team is separate and has its own scheduling then they might be interested to know how much testing time you (the developers) think is needed from them on a given ticket. They might ignore your numbers and put their own in. Either way they can track that separately from the dev time estimates.
On the other hand, if one team is doing all the dev, testing, and QA, and the purpose of the time estimates is to predict and plan what that team is doing in a particular time frame, then of course the time estimates must include QA, along with any other tasks that it is necessary for that team to do in order to achieve the stated goal. For that matter if you have to have a kick-off meeting for every ticket, or fill in some bit of paperwork at completion, then the time for the admin needs to be in there somewhere. You can't just ignore it.
If it's all one team but with separated roles "developers" and "testers", then that might mean you have a lot of tickets that only one side of the divide is capable of working on, and your (perhaps entirely hypothetical) Gantt chart looks exactly like the chart for two separate teams would look. This fact will upset some methodologies more than others, and you might be better off splitting the planning because of that, but if you don't split it then you have to ticket and estimate everything the team needs to do or your predictions will be hopeless.
If the purpose of the estimates is something other than prediction and planning, for example "because we mindlessly follow an empty ritual that includes them", or "because management uses them as a stick to beat us with to get overtime out of us", or "because we have to make a fixed-price bid and the numbers go into an enormous formula" (thanks John Wu), then it might be harder to figure out what they should include ;-)