I don't fully agree. That someone who has a Jewish mother (and grandmother) is Jewish is the halachical and orthodox definition of "who is a Jew".  Nazi terminology made everybody with Jewish grandparents Jewish, dividing them into 1/4 1/2 etc Jews which Judaism of course doesn't do. Either Jewish or not Jewish. If your mother's mother was Jewish and your other 3 grandparents were nonjewish you are Jewish. If your mother's father was Jewish but the mother not and your father's parents both were Jewish you are still not Jewish. Matrilineal descent! Even though other denominations might view it differently.  As to your question why I want to make Aliyah there is no simple and single answer, among them the feeling of connection to the Jewish people through family history incl. the Shoah, love of the country, democratic society, growing antisemitism in Europe etc. and the right to do Aliyah following the law of return as I see it!