I believe the text says hillsides not mountains. Also, this would mean all people would be of Noah, which seems to create problems within itself. But basically I believe the reason for the Flood was solely to kill the Giants in Gen 6:1-8, whom were the abominable to God, offspring of Adam's daughters and the fallen angels.
Well let us look at what God said about it:
Genesis 6:5-7
King James Version
5 And God saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually.
6 And it repented the Lord that he had made man on the earth, and it grieved him at his heart.
7 And the Lord said, I will destroy man whom I have created from the face of the earth; both man, and beast, and the creeping thing, and the fowls of the air; for it repenteth me that I have made them.
Genesis 7:17-24
King James Version
17 And the flood was forty days upon the earth; and the waters increased, and bare up the ark, and it was lift up above the earth.
18 And the waters prevailed, and were increased greatly upon the earth; and the ark went upon the face of the waters.
19 And the waters prevailed exceedingly upon the earth; and all the high hills, that were under the whole heaven, were covered.
20 Fifteen cubits upward did the waters prevail; and the mountains were covered.
21 And all flesh died that moved upon the earth, both of fowl, and of cattle, and of beast, and of every creeping thing that creepeth upon the earth, and every man:
22 All in whose nostrils was the breath of life, of all that was in the dry land, died.
23 And every living substance was destroyed which was upon the face of the ground, both man, and cattle, and the creeping things, and the fowl of the heaven; and they were destroyed from the earth: and Noah only remained alive, and they that were with him in the ark.
24 And the waters prevailed upon the earth an hundred and fifty days.
Problem with the local flood false hypothesis is that animals would flee and so wouldn't people if the waters were just desatroying a specific area. Birds can fly and most land animals have an instinct to flee when calamity is approaching.
Also as it rained and the fountains of the deep were gushing water for forty days- people could flee as well to another region, so that idea doesn't hold water ( all pun intended).
As for teh high hills and mountains both hills and mountains is the word "har" and mean mountains and mountain ranges.
Once again they were covered by 22 1/2 feet of water. A local flood will not cover mountains by 22 1/2 feet of water. The water would just flow down the other sides of the mountains in to the next lower areas!
