I mean, saying it would take half of forever with existing technology, when we do not have the technology to do it in the first place, seems a bit redundant. There are any number of hypothetical technologies for travel to relatively nearby stars that, while we don't have them presently, at least do not violate physics and are more an issue of requiring a civilization of much larger scale than ours to afford to build them rather than one of if they're physically possible.

An analogy I once saw was this: suppose you were to go back in time to meet a medieval blacksmith, and you show him the blueprints for a modern jetliner. You might, with a lot of explaining of the relevant physics and engineering behind all the parts, be able to convince the guy that the machine could work if constructed. But, he'd have no idea of the process for how many of the parts are made, or the materials they're made from, and if you included all that information too, the whole process would be so expensive and the size of the economy back then so small that in all likelihood, not even the richest kingdom on earth in his day could possibly afford to actually build and operate one. However, if the blacksmith took all that information and concluded "this can never happen, it's just too hard", time would prove him wrong.