Here's why:
* Synchronizers' Role: Synchronizers are components within the transmission that match the speed of the gears before they engage. When you shift, the synchronizer slowly brings the speed of the input shaft (connected to the engine) to match the speed of the selected gear. This allows for smooth engagement.
* Grinding: Grinding occurs when you try to force the gears together while their speeds are significantly different. This damages the synchronizer cones and rings, creating friction and wear.
* Squealing After Grinding: The squealing sound is the result of this damaged friction material. The roughened surfaces are now constantly scraping against each other, even when the gear is engaged, producing a high-pitched squeal, especially under load (acceleration).
Other less likely, but possible, contributing factors (though usually accompanied by other symptoms):
* Low Transmission Fluid: While low fluid wouldn't directly *cause* the squeal from a previously ground gear, it exacerbates the problem by reducing lubrication and increasing friction, potentially making the squeal louder and more persistent.
* Damaged Gear Teeth: Severe grinding can damage the gear teeth themselves. This is less likely to be the *primary* source of the squeal after the fact, but it could contribute if the damage is significant.
In short: The squealing is a clear indication of transmission damage likely caused by the initial grinding. Ignoring this could lead to more serious and expensive transmission problems down the line. You should have a mechanic inspect your transmission as soon as possible.