Like an eagle that stirs up its nest: of the four lines in this verse, the meaning of this line is the most difficult to determine. New Revised Standard Version is the same as Revised Standard Version; other renderings are New Jewish Publication Society’s Tanakh “Like an eagle who rouses his nestlings,” BÍBLIA para todos Edição Comum “like an eagle keeping watch over its young who are in the nest,” New Jerusalem Bible “Like an eagle watching its nest,” Revised English Bible “As an eagle watches over its young.” The Hebrew verb usually means to “disturb” or “stir up”; but the meaning “watch” found in the Septuagint is defended by some and is the meaning given by Revised English Bible and New Jerusalem Bible, and it is an alternative rendering given in the Good News Translation footnote. This meaning is the one recommended here. So we may also say something like “Yahweh is like an eagle watching over its young in the nest.”

An eagle: in cultures where eagles are unknown, some other large bird of prey may be used.

That flutters over its young: the verb in this line is the same one used in Gen 1.2 of the spirit (or, wind) of God hovering over the abyss. Good News Translation “teaching its young to fly” (also Contemporary English Version) follows theVulgate, provocans ad volandum, “enticing [its young] to fly.” This, however, is most unlikely, and it is recommended that the Revised Standard Version rendering be followed.

Spreading out its wings, catching them: Revised Standard Version and other translations take this line and the next one to apply to the eagle and its young. But a number of commentaries and translations take this line and the next one to apply to Yahweh and his people, not to the eagle and its young. So New Jewish Publication Society’s Tanakh says “so did he spread his wings and take them” (also Osty-Trinquet, Pléiade).

The last line, bearing them on its pinions, therefore refers also to God, not to the eagle. So God “carries them on his wings”; the Hebrew word for “wings” here is different from the one used in the previous line. For the figure of God doing this for his people, see Exo 19.4.

A possible alternative translation model for this verse is:

• The LORD is like an eagle guarding its nest,
and hovering over its young.
The LORD is always ready to spread his wings
and catch his people when they are falling.

Quoted with permission from Bratcher, Robert G. and Hatton, Howard A. A Handbook on Deuteronomy. (UBS Helps for Translators). New York: UBS, 2000. For this and other handbooks for translators see here .

There are a number of problems in verse 11. In the Hebrew poem verses 10 and 11 are closely linked, so that the main thought of verse 10 is continued in verse 11. In verse 10 the last three verbs are “shielded or, encircled, cared for, guarded.” In this context the translation of verse 11 as “stirs up its nest” (RSV, NIV) is not likely. “Watches over its nest” (NEB, JB, REB) is a better exegesis, but this verb is often translated elsewhere as encourage so “encourages its nestlings” is entirely possible (see NAB).

All of the English versions misrepresent how an eagle teaches its young to fly, probably because they accept the hypothetical myth mentioned above, namely that eagles carry their young on their wings.

What actually happens is that young eagles are shown by their parents how to set their wings by spreading them when the wind blows, while holding on to the side of the nest. Eventually when the young eagles have mastered this, they let go and ride the wind out of the nest. At this stage the parent eagles are usually nearby, circling overhead.
The Hebrew text, if the myth hypothesis is rejected, is actually open to a very different interpretation that is in accordance with what really happens. Th
is interpretation has some scholarly support, but has not yet been mentioned in any commentary or translation. It involves interpreting the last verb in verse 11 as meaning “lifts himself up” rather than “is lifted up.” The following model gives this interpretation:

10 He found him in a desert land,
in a barren howling waste.
He circled around him, cared for him,
guarded him like the apple of his eye.
11 Like an eagle encouraging its nestling,
hovering over its offspring,
spreading its wings, instructing him,
until he rises up on his strong wings,
12 Yahweh alone guided Israel,
with no foreign god at his side.

In verse 11 there are two words for “wing”, the second of which is a poetic word derived from a Hebrew root meaning “mighty”.

Source: All Creatures Great and Small: Living things in the Bible (UBS Helps for Translators)