You need to specify a condition, not just a value, for the FILTER function.

So:

=FILTER(A2:A6, B2:B6 = MAX(B2:B6))

I have set up a demonstration spreadsheet for this, feel free to have a look or copy it.

Short answer

Use REGEXMATCH(text, regular_expression) instead of = or EQ(value1,value2) to set the conditions for FILTER(range,condition1,[condition2, ...])

Demostration

Data source

+---+---------+---------+
|   |    A    |    B    |
+---+---------+---------+
| 1 | Field 1 | Field 2 |
| 2 | Yes     | A       |
| 3 | YES     | B       |
| 4 | no      | C       |
| 5 | No      | D       |
| 6 | NO      | E       |
| 7 | yes     | F       |
+---+---------+---------+

Formula in D1

=FILTER(A2:B7,REGEXMATCH(A2:A7,"^yes$"))

(The word is placed between ^ and $, so that the entire cell content is required to match it.)

Result

+---+-----+---+
|   |  D  | E |
+---+-----+---+
| 1 | yes | F |
+---+-----+---+