Avocados are frequently bad in one or both of two ways:
- "Bruising" where the flesh turns dark brown/black, is squishy and has a sour smell;
- "Fibrousness" where the flesh gets full of green or brown fibers.
In the bruising case, you can eat the rest of the flesh if you can cut out the bruises, at least until it takes over the avocado, and then you compost it. Bruising is caused by basic rot.
In your case, though, you're seeing the fruit's fibers from when it formed, because of being picked too young, or coming from a stressed tree, or just as a mutation. Per California Avocados:
Strings or stringy fruit or the thickening of the vascular bundles (fibers that run longitudinally through the fruit) are generally the result of fruit from younger trees or improper storage conditions. Often times the fibers or strings will disappear or become less noticeable as the fruit (and tree) matures.
These strings are harmless, but they can impair the taste and texture of the avocado, so I'd recommend giving it a taste to decide if you can still use it. It also depends partly on what you're using it in, and how you plan to process it.