grammar - What is meaning of 「〜ないように思えてなりません」?

Can somebody explain the grammar and meaning of this expression in the sentence below? It may be just my poor understanding of how なりません functions in the language but I'd appreciate an explanation.

I have added my own translation and placed the previous sentence in [ ] to indicate context.

[人間を人類というより大きな範疇（＝カテゴリー）でみても、人間は「かろうじて生きている」のが現状ではないかと思う。しかし、]

人類はそうやすやすと滅びないように思えてなりません。

[Even if I look at the human beings from wider perspective than as a members of the human race, it seems to me that humans are only just surviving. However,]

I have to think that the human race will not be that easily defeated.

For full context see: 中上級のにほんご Dec 2013, p37

My grammatical logic________________

I have translated the whole expression as 'I have to think'(~ I cannot help coming to the conclusion that..?) but when I compare to expressions such as ~なければならない (ie must) this does not seem logical. For example:

If : ~滅びると思いません　＜〜＞　滅びないと思います

Then ~滅びると思ってなりません　　＜〜＞　滅びないと思わなけばなりません

Answer

It's a little tricky since it's using two expressions that seem like they could be one thing but are another. We may be able to think of 思える as its own word, meaning basically what you'd expect, to feel something will be a certain way. Then take it in the てならない structure, which in this case means "can't help (feeling this way)" (and not the "have to" meaning we can sometimes get from ～て（は）ならない). It's like "no matter how I look at it I can't see it being any other way," そのように思えて仕方がない.

But it's a kind of set phrase anyway, so if you just remember 思えてならない as its own unit meaning "can't help but feel," you'll be fine. 思えてならない (in plain form) even has its own edict entry!

So with that in mind, we can reinterpret that sentence as saying:

However, I can't help feeling that humanity won't fall so easily.

Or, you know, something along those lines. You may want to review the てならない grammar pattern to help you keep it separate from the しなくてはならない. The latter also usually has a は in it, and I feel might more commonly be phrased with いけない (but don't quote me on that one).