As a Jew I agree with you. She should be putting her “American” best foot forward and while she may admire Israel, she is hoping to be a Chief Justice of the USA and not be so enamoured with Israeli Justice Barak who was a demagogue of the worst kind!
Justice Barak has single handedly struck down Israel's identity as a Jewish state in favor of his definition of a democratic state. Here is an excellent review of his philosophy by Nathan J. Diament Director, Institute for Public Affairs Union of Orthodox Jewish Congregations of America.
Kagan's support for Barak's juridical philosophy means that she will stand for the internationalization of US law.
Barak believed that every human activity is under the rule of the courts. There can be no more infamous belief. This is profoundly dangerous appointee.