IQueryable WHERE inside a for loop does not produce expected result

Objective:

Implementing AND filter. Where users input list of keywords in an input, then the list gets filtered based on the first word, then the next and so on. For instance, when they input "May", their list should be filtered to show only records for the month of may. In case, they input "May June", they should get empty list. Because, you shouldn't find records for the month of June within a list for the month of May

My failed attempt:

Below example does not work as I expected to

List<string> keywords; // e.g. "May", "June"

for (int i = 0; i < keywords.Length; i++) {                
    string searchTerm = keywords[i];
    entityObj = entityObj.Where(x =>
            x.Month.ToLower().Contains(searchTerm) ||
            x.Year.ToString().ToLower().Contains(searchTerm) ||
            x.Product.ToLower().Contains(searchTerm));
}

entityObj is of type IQueryable<SomeEntity>. Assume there is a table in the database with Month, Year and Product columns. On the first iteration, searchTerm will have May as its value. So, entityObj should return IQueryable object for records that only has May in the Month column. I expect the second iteration to return nothing, since we are looking for value of June in a result of the previous iteration which has only May result. However, I am getting records that have June value instead. No matter how many keywords I have, it is always returning the result based on the last element in the list which is the last iteration.

When I do below

string searchTerm = "May";
entityObj = entityObj.Where(x =>
            x.Month.ToLower().Contains(searchTerm) ||
            x.Year.ToString().ToLower().Contains(searchTerm) ||
            x.Product.ToLower().Contains(searchTerm));

searchTerm = "June";
entityObj = entityObj.Where(x =>
            x.Month.ToLower().Contains(searchTerm) ||
            x.Year.ToString().ToLower().Contains(searchTerm) ||
            x.Product.ToLower().Contains(searchTerm));

I get the result that I expect, empty list. However, When I do that inside a for loop, it does not work. Am I missing something here?