I'm currently learning biology at my school, and Gregor Mendel is a name I'm very familiar with. But I've just learned today that his Inheritance Theory wasn't accepted at first by scientists of the 1800s. I've also heard that it was only accepted 16 years after he died, and now my question is, why did scientists during Mendel's time not accept his Inheritance Theory?
Mendel's theory wasn't rejected at the time. It was seen as a special case for certain characteristics only, characteristics where there were two distinct forms with no intermediate states. For example, Mendel's peas came in yellow and green varieties (i.e., the colour of the seeds); there weren't intermediate yellow-green peas.
Mendelian inheritance describes features controlled by single genes. Many characteristics are controlled by multiple genes, and don't follow Mendel's rules. For example, a human with a light-skinned parent and a dark-skinned parent will often have medium skin, intermediate between light and dark. This type of characteristic, with intermediate states, is very common, and Mendelian inheritance doesn't explain it.
Mendel himself was aware of this, and didn't present his theory as a general theory of inheritance. As a theory of inheritance that only worked for special cases, Mendel's theory simply wasn't very interesting for most people working on the problem of how inheritance worked. People read it, and forgot about it.
Mendelian inheritance became a controversial thing in about 1900, when his work was rediscovered. The biggest proponent of Mendelian inheritance was William Bateson, who'd been working on inheritance in the late 1800s, noting that there were many "Mendelian" characteristics, with two distinct states and without intermediate states. At that time, he didn't know about Mendel's experiments, and recommended that that type of experiment be performed. The idea that Mendelian inheritance, with distinct states, might be a general case rather than a specific case only applying to certain characteristics, was controversial, and many did reject it as a general case, because it wasn't clear whether it could explain continuous variation in characteristics.
An important step towards wider acceptance of Mendelian inheritance was the work of Ronald Fisher, who showed that if a characteristic was controlled by multiple Mendelian factors (i.e., genes), continuous variation as observed could result:
This, and more experiments, and eventually the discovery of how genes work, made Mendelian inheritance the standard theory (with modification for multiple genes controlling many characteristics, and some other exceptions).
If you're interesting in reading Bateson's work, there is a good bibliography at https://en.wikipedia.org/wiki/William_Bateson#Publications