The root cause (no pun intended) is that excess nitrogen will make the roots fork.
I've heard two different theories as to why: "Hot" fertilizer like fresh manure burns off the fresh roots and makes them fork.
A lot of nitrogen in shallow soil fails to encourage the plant to scavenge deep in the soil for nutrients, and they send out roots sideways instead.
Or it could be combination of the two -- but the latter came from a more reliable source and fits more with my experience.
(One of my books versus something seen on the internet -- sorry I can't remember exact sources.)
Even in soil where I haven't added extra nitrogen but was very fertile with other nutrients, I have seen carrots develop not so much forked roots as fat sideways roots instead of the usual fine "hairs".
gardening.stackexchange.com/users/51/bstpierre
Fresh manure can cause carrots to fork.
If you use any fertilizer, make sure it's well-rotted manure instead.
( source )
I've read that the same goes for beets as well.
gardening.stackexchange.com/users/6/Doresoom
I grow carrots and I don't believe roots branching off has anything to do with manure.i use kelp for manure.
I sift my soil and mix it with sand
and I have perfect 16 to 18in carrots every time with no roots branching off.
Prior to doing this I didn't sift my soil or mix with sand and my carrots had branches everywhere.
I think the branches on carrots are caused by hard soil
gardening.stackexchange.com/users/11331/Ben
Fresh manure also can transfer E. Coli to garden vegetables, so you should always make sure your manure is well composted, for around 3-4 months.
If it's still smells very strongly, it's probably too fresh.
gardening.stackexchange.com/users/6944/Jeff-Inventor ChromeOS
Leads to forking of the tap roots (which are the carrots)Leads to high vegetative growth leading to small tap roots (carrots)
gardening.stackexchange.com/users/15603/B. O. Wangao
It's said that we shouldn't use manure when preparing ground intended for carrots. Is it that carrots don't thrive on manure, or is it that they fork and splinter too much?  What about other roots? Radishes, beetroots etc?
Why are we instructed not to use manure before planting carrots?
gardening.stackexchange.com
<vegetables><manure><carrots><root-vegetables>
gardening.stackexchange.com/questions/123
gardening.stackexchange.com/users/99/Tea Drinker
Excess nitrogen will make roots fook. The plants no longer need to dig deep for nutrients so they grow sideways roots instead. Excess nitrogen in shallow soil fails to encourage the plant to scavenge deep in the soil for nutrients, and they send out roots sideways instead and fork. Fresh manure also can transfer E. Coli to garden vegetables.
Excess nitrogen in shallow soil fails to encourage the plant to scavenge deep in the soil for nutrients, and they send out roots sideways instead and fork  Fresh manure also can transfer E. Coli to garden vegetables.