Why <big> is not in HTML 5 Tag list while <small> is?

<small> is used more frequently, for footnotes and such...with <h1>, <h2> and <h3> there just wasn't a use for <big>, hence why it's removed.

Some purely presentational tags managed to slip through into the spec before but the 2 standards bodies have finally reached a concesus to remove all purely presentational tags in favour of using CSS. If something has no semantic value and is purely for visual apearance - it does NOT belong in the markup - it belongs in a stylesheet.

Remember, the tags are meant to be semantic, not presentational. There is such a thing in English as "fine print". This is what the small tag represents. There is no analogous concept of "big print" except for a header, which is already covered by seven other tags.

The same logic that applies to small (as "fine print") is also just as true for big (as "warning"). Public postings, mostly, but also manuals or even contracts often have things written in bigger fonts that signify [so... semantics!] a warning.

It's not the same as emphasis, which has a meaning in context, but rather "whatever you skip in this text, this part you should read because it's not the usual blah blah but something with immediate and important consequences"

That's why I think big and small should both be out or both in.