Why everyone says that the end of QE drives a bond sell-off?

The QE keeps yields low because it is used to buy bonds. Yields raise to attract buyers. Let's say you have a 2% yield bond now, QE ends and the government has to attract new investors and raises the yield on the new bonds at 4%. Chances are you will sell the 2% bond and buy the 4% bond.

Supply and demand.

QE is currently the largest buyer of bonds. Remove the largest buyer, overall demand for bonds drops, which causes bond prices to drop.

As always there are two ways of looking at this.
Either,end of QE means economy has recovered or,
End of QE means less cheap money therefore economy could slow.
If less cheap money then rates go up, bond prices go down.
Economy slows, less demand for money, rates go down, bond prices go up.
Economy recovering then risk-on in equities. More buyers of equities = more sellers of bonds.

Yellen took office. The end of QE is coming.