The rubber coated seal needs to be and should be lubricated for installation. There also probably is a slight burr on the end of the shaft where the lever goes against which needs to be dealt with for the installation tool to fit over since it is a close fit. Some sort of sleeve should be used over the shaft if possible as well. The BMW version of the seal installer comes with plastic sleeves.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)