Do you mean a culture-wide version of the End of History Illusion (http://m.psychologytoday.com/blog/reality-play/201301/the-end-history-illusion)?

It is called having a "telos", or working under the paradigm of a teleological framework. For example, some archaeologists and for that matter historians working under the theoretical underpinnings of the direct historical approach assumed that they can reconstruct history starting from the present and slowly deconstructing it ( and by this I mean downgrading society to what they assumed to be the core of such society). As you can see, this is the reverse of the way history unfolds. the direct historical approach, and any other kind of teleological argument, wrongly assumes that it knows the end of the story and that everything gravitated towards accomplishing such goal, such telos.

I think your question could use some clarification because it's so vague it could tie into anything. In what sense do you think people believe they're at the highest point in history? Do you claim that people tend to think they are genuinely better people now than people in the past were, or just that our society is better to live in? The title implies one and the text implies the other. Since the question is basically about the present, is it even really historical?

I find allot of people have trouble believing the future will be differant. Nor do they think that their goals will change and thus make many current decisions that do not reflect what their future may want or be. Then when you go past our lifespan, it starts to become incomprehensible but that future will be as real as you and me are right now.

One example I use is the English language (or any language) and why it matters little if it is the dominant language in a few hundred years. There may be a language called english but chances are it and the culture around it will have evolved so much that you or me would have little chance of understanding it.