This is from an avid Shakespeare actor/reader, I've always believed he wrote the plays, but is there significant evidence that could make a strong argument otherwise?
If you really want to sharpen your tools against authorship arguments, you will find many of them here:
hi! there's always room for more discussion, but there have been a few threads on this. catch up on previous responses here
Is there any solid evidence that Shakespeare's works were written by others?
What are some of the arguments against Shakespeare's authorship?
None. The methods we use to attribute the plays and the poems to Shakespeare are exactly the same as those used to attribute works to any author. All the relevant historical records support the attribution, the only rebuttal is that the historical record is forged. Read "How We Know That Shakespeare Wrote Shakespeare: The Historical Facts". Another good summary of the historical record is at Wikipedia: https://en.wikipedia.org/wiki/Shakespeare_authorship_question#Case_for_Shakespeare.27s_authorship
Shakespeare is such an integral part of our culture that it would be strange if nobody did question his authorship. Unfortunately, those who say he didn't throw out everything we know about history and put ridiculous comic-book scenarios in its place. Just the idea that plays and theatres were so important is an anachronism.