Did you set object and key correctly? also Did you use NSDictionary and NSMutableDictionary correctly?
I checked your below code first.
NSMutableArray *testArray=[NSMutableArray arrayWithObjects:@"Jan Month",@"Feb Month",@"Mar Month",@"Apr Month",@"May Month",@"June Month",@"July Month",@"Aug Month",@"Sep Month",@"Oct Month", nil];
NSMutableArray *testResult=[NSMutableArray arrayWithObjects:@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass", nil];
NSDictionary *testDetails=[NSDictionary dictionaryWithObjects:testArray forKeys:testResult];
[testDetails setValue:@"Fail" forKey:@"Feb Month"];
Now see the result.There is only 1 key value pair

What your mistake here is you wrongly set the key and object as well as you need to set the value to NSMutableDictionary.
If you want to edit the values in dictionary you must use NSMutableDictionary as it is mutable.Using NSDictionary you cant edit because it is immutable.You can't change anything.
NSMutableArray *testArray=[NSMutableArray arrayWithObjects:@"Jan Month",@"Feb Month",@"Mar Month",@"Apr Month",@"May Month",@"June Month",@"July Month",@"Aug Month",@"Sep Month",@"Oct Month", nil];
NSMutableArray *testResult=[NSMutableArray arrayWithObjects:@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass",@"Pass", nil];
NSMutableDictionary *testDetails=[NSMutableDictionary dictionaryWithObjects:testResult forKeys:testArray];
[testDetails setValue:@"Fail" forKey:@"Feb Month"];
Now see the printed result
Printing description of testDetails:
{
"Apr Month" = Pass;
"Aug Month" = Pass;
"Feb Month" = Fail;
"Jan Month" = Pass;
"July Month" = Pass;
"June Month" = Pass;
"Mar Month" = Pass;
"May Month" = Pass;
"Oct Month" = Pass;
"Sep Month" = Pass;
}
Also see the below screenshot

You should know to use the dictionary first.
Apple NSDictionary API reference says
The NSDictionary class declares the programmatic interface to objects that manage immutable associations of keys and values. Use this class or its subclass NSMutableDictionary when you need a convenient and efficient way to retrieve data associated with an arbitrary key. NSDictionary creates static dictionaries, and NSMutableDictionary creates dynamic dictionaries. (For convenience, the term dictionary refers to any instance of one of these classes without specifying its exact class membership.)
Apple NSMutableDictionary API reference says
The NSMutableDictionary class declares the programmatic interface to objects that manage mutable associations of keys and values. It adds modification operations to the basic operations it inherits from NSDictionary.
NSDictionary vs NSMutableDictionary