Troubleshooting with anchor points
While trying to add a new anchor point to an intersection it adds it in another place, some pixels to the left. Basically, it happens whenever I try to use the pen tool. At the same time looks like whenever I move an object it doesn't go exactly where I want it to. Basically, no overlapping or adding anchor point to an existing vector.
Please accept my sincere apology for the inconvenience. Please get in touch with us at any of the other support channels – https://helpx.adobe.com/support.html . Since this is not a generic issue that we can reproduce at our end, we will need someone to look into your machine to figure out what is going on here.
Thanks & Regards,
View > Uncheck "Snap to Pixel"
Ashutosh Gupta (Illustrator Team) commented
Shift + Click using the pen tool would help you clicking over the intersection.
Thanks and Regards