No, I haven't been told this. Young children might start to imitate your stutter, cause in some age they just imitate everything as part of learning and observing the world. But even that won't stick with them and is not actual stuttering. Maybe your friend has a speech impediment of their own, they just consciously or subconsciously hide it and speaking with you made them have to face it, be anxious and fail to cover it. Or they just are that easily influenced. People will adapt to the dialect, communication patterns of their peers, that's normal, but again they can't develop stuttering from interacting with somebody who stutters. Stuttering is for most people neurologically rooted. Sadly, some people still believe in stuttering being contagious, despite this being disproven. If they are that uncomfortable and insecure being around you, you might want to rethink that friendship tbh.