It's cool that you said this because for some people this statement is part of why people believe this way. My brother wrote his master's thesis on this subject. The hypotheses (or was it the theory? I get confused) in his essay went like this:
Does God have the ability to save everyone? Yes Does God desire that everyone be saved and be with him? Yes. Ipso facto God's will be done always.
So though there are many verses that say "the only way to the father is through the son" There are also verses like this one :
1 John 2:2"He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world." (NIV)
There are more verses with a similar message like:
Romans 11:32
"For God has bound all men over to disobedience so that he may have mercy on them all." (NIV)
From Wikipedia about a word that was mistranslated in the Latin Vulgate
Christian universalists point towards the mistranslations of the Greek word αιών (Lit. aion), as giving rise to the idea of Eternal Hell, and the idea that some people will not be saved.[14][25][26]
This Greek word is the origin of the modern English word aeon, which refers to a period of time or an epoch.
The 19th century theologian Marvin Vincent wrote about the word aion, and the supposed connotations of "eternal" or "temporal":
Aion, transliterated aeon, is a period of longer or shorter duration, having a beginning and an end, and complete in itself. [...] Neither the noun nor the adjective, in themselves, carry the sense of endless or everlasting."
So based on this and there is more information like this. Another half a dozen Bible verses or so could lead anyone to the conclusion that God has the option of saving anyone if not everyone.
This topic really gets people fired up because in their mind they know for a fact only people like them can go to heaven. There are verses in the Bible that say they are correct in that thinking. It's probably the biggest contradiction in the Bible
But oh no! It's impossible for the Bible to contain contradictions. Well, there is are contradictions just above. Personally, I just let God figure all of that out and I try to do the right thing, putting my fate in God's hands where it belongs.