The most difficult mathematics is that which you do not know. A surprising amount of mathematics is actually easy once you've learned it. Of course, once you learn the easy stuff, then you have to start tacking the deep stuff, and that gets harder.
An isosceles triangle has two sides of equal length. An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the isosceles triangle theorem, which was known by Euclid.
An equilateral triangle is isosceles because it has three equal sides and an isosceles must have two, which an equilateral does. However, an isosceles has 2 equal sides and therefore is not an equilateral because an equilateral must have 3 equal sides. Simply: an equilateral triangle is an isosceles triangle because 3 is greater than or equal to 2 and an isosceles triangle is not an equilateral triangle because 2 is not greater than or equal to 3. Hope this helps.