Why Logistic regression into Spark Mllib does not use Maximum likelihood estimation?
I think you're confused. Maximum likelihood is a general technique for giving the most likely parameter estimation. There is no closed solution for maximum likelihood for logistic regression, so both R and Spark must numerically estimate it. 

How exactly the likelihood is estimated could be slightly different and might depends on the implementation. For example, Spark prefers to add regularization, R might like to use something else (you'll need to check the documentation).

Summary: Both R and Spark try to estimate ML for you. Please check the R documentation on how R do it.