Please forgive me if this is stupid/common sense/been asked a million times before, I'm an amateur. I've recently seen an explanation for why time travel wouldn't be possible which is roughly this: If you travelled from Point A to Point B at the speed of light for 1 year from the perspective of people remaining at point A then no time would have elapsed as per the traveller's perspective. If on arrival you look at Point A then you would see it as the same as when you left. Then by travelling back for 1 year then you simply would have caught up with those at Point A (Presumably because light coming towards you along with the traveller's speed of return would balance out.

My question is this: What if you introduced a Point C along the shortest length of an isosceles triangle. The base of which being Point A - Point C (shortest length) and Point A - B and Point B - C being the longer lengths.

If from the perspective of the person at Point A you travelled at light speed for 1 year, then without looking back travelled for 1 year to Point C, then 2 years would have elapsed but no time for the traveller. If you looked from Point C to Point A which is shorter than 1 year, do you look back on the past?!

Well this case is no particular one but when you see something that needs light years to reach you you just see the light that has been travelling since a few years ago so you always take late info about the points you look at.