Short answer, you have an alignment issue.
Generally it's a wheel tracking problem, but the causes can be complex, including poor wheel dish, wheels not on a common plane, wheels not vertical in frame, or some combination of the above. It could also be that your center of gravity isn't on the bikes central plane, so you have to lean to get the yourself over the wheel track.
Before you go crazy, test the bike in a parking lot. Most roads are crowned, and bike geometry is such that they turn uphill if riding across a slope, so there's a slight pull to the left on crowned roads. It's slight, and you probably aren't posting about that, but should rule it out before starting in on the complex alignment checks.
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