Does it sometimes take energy to create a chemical bond? Wikipedia says so:


  Bonds can also be broken apart. Since most bonds require energy to form, they also give off energy when they are broken. But before most bonds break, the molecule has to be heated. Then the atoms start to move, and when they move too much, the bond breaks. Molecules that require less energy to break than they give off when broken are called fuels. For example, a candle will just sit there and nothing happens. But when you use a match to light it, it will burn for a long time. The match brings the energy to break the first bonds, which release enough energy to break the bonds below them, until the candle has burned down.
  But what I have learned is bonds release energy when formed.
"Molecules that require less energy to break than they give off when broken are called fuels." is the most imprecise sentence in the paragraph, because fuels don't give off energy when their bonds are broken, but when these broken bonds form new bonds (with oxygen) that are much more stable and release more energy than it took to break the original (carbon-hydrogen) bonds.

A candle is stable in air, even tho it does not have complete stability in an oxygen-containing atmosphere. But if you put sufficient energy into a few bonds, the excited atoms will combine with oxygen, which gives off enough energy to excite a few more bonds, which etc., etc. It's this new reaction, which is overlooked in the paragraph, which provides the increased temperature during the reaction.

The energy that "bonds require to form" is an activation energy which destabilizes a molecule enough so that it can reorganize with other reagents (like O2) to form more stable products. This activation energy may be supplied initially from outside sources (the match), but in a continuing reaction, the exotherm from the reaction provides the activation energy and then some.