Is it normal for wood to sometimes squeal when screwing into it?
Yes, sometimes you may encounter a stud that has a big knot or some really gnarly grain that make it can be really hard to insert a screw. Knots especially can be exceedingly hard. A squeal is also rather common in such instances.

You did the right thing by backing out the screw and drilling a slightly larger pilot hole. Doing so you prevented the possibility of over stressing the screw and either stripping out the head or twisting it off. There are some additional things to consider in such case:


If possible move where the screw is being inserted to try to bypass the knot.
The backed out screw may very well have been over stressed when attempting the install it the first time. It should be discarded and use a new screw on the second trial. 
Often it can be useful to lubricate the threads of the screw to allow it to enter the wood with less torque. This can also reduce or eliminate the squeal that you were hearing. A common method to lubricate the threads of the screw is to rub them across a bar of hand soap before driving the screw into the hole.