It is important, if you’re using a dipole antenna fed with open wire line feeders, to try and keep the antenna balanced. The first rule is to make sure both sides of the antenna are the same physical length. Sometimes, even when doing that, the antenna will not be balanced due to the asymmetrical issue. If one end of the antenna is not the same distance above ground as the opposite side, that may cause an electrical imbalance. Objects that are close to the antenna can cause some imbalance. Some of this we have control of and some of these physical issues causing an imbalance we have no control over. First off, make sure you have the same amount of wire each side of the center insulator.
In a well designed open wire line fed antenna that is balanced, the feedline will not radiate! The open wire line feedline, should not radiate! When the antenna is balanced, the current in each leg of the feedline will be equal, but 180 degrees out of phase. It’s the equal amplitude and 180 degrees out of phase that keeps the feedline from radiating. Feedline radiation in or near the shack can cause all sorts of issues, including RF in the audio of your HF rig. In a smaller way, it will cause the radiation pattern of the antenna to deviate from the text book model due to feedline radiation, although, that in my eyes is no big deal.