Perhaps their misunderstanding comes from a poor grasp of the English language or a failure to even take the time to read the Biblical text, but what the verse actually says is that Jesus cried out, "Eli Eli lama sabachthani!"
Not "cried," but "cried out," as in shouted.
Jesus did not say those very important words while weeping copious tears.
This is the Greek of Matthew 27:46...
27:46 περὶ δὲ τὴν ἐννάτην ὥραν ἀνεβόησεν ὁ Ἰησοῦς φωνῇ μεγάλῃ λέγων, Ηλι ηλι λαμὰ σαβαχθανι τοῦτ᾽ ἔστιν Θεέ μου θεέ μου ἱνατί με ἐγκατέλιπες
Here is the phrase we're examining:
word Greek transliteration
Jesus Ἰησοῦς Iēsous
cried ἀναβοάω anaboaō
with a loud μέγας megas
voice φωνή phōnē
Do you see those last two Greek transliterated words, "megas phone?"
Those are the words from which we get the name for the device that amplifies the human voice, a device which a person uses to speak loudly.
That is what Jesus did...
when He "anaboaō megas phōnē."
He spoke those words loudly.
Rather than saying them in tears, Jesus shouted the first words of Psalm 22 to call the attention of the Jews around Him at the cross to the fact that their Messiah was fulfilling His mission as outlined in the Psalm.
In contrast, when Jesus saw Mary's sorrow at the death of Lazarus in John 11, He was moved with compassion and He did weep, but the Greek word used to describe His weeping there was "δακρύω" or dakryō, not our anaboaō.
Jesus continued to fulfill one verse after another of Psalm 22 at the cross, proving the prophecies sung in the Psalm by King David a thousand years before Messiah.
Then, at precisely the time of the Temple sacrifice, Jesus spoke again, saying: "It is finished!" (John 19:30)
His work done, Jesus yielded His spirit unto the Father, breathed His last and died. The Gospel of Matthew tells us what happened next:
"Suddenly, the curtain of the sanctuary was split in two from top to bottom; the earth quaked and the rocks were split." (Matthew 27:51)
The Messiah's Mission had been accomplished, man's sins atoned for in the perfect sacrifice of the Lamb of God. Three days later, Yeshua, whose means "The Lord Saves," rose again from the grave, just as He had promised.
King David picks up from that point once again in Psalm 22 as he prophesied:
"All the ends of the earth will remember and turn to the Lord. All the families of the nations will bow down before You, for kingship belongs to the Lord; He rules over the nations.
All who prosper on earth will eat and bow down; all those who go down to the dust will kneel before Him— even the one who cannot preserve his life." Psalm 22:27-29
The Day is fast approaching when every knee will bow and every tongue confess that Jesus Christ is Lord, to the glory of God the Father.
Dear reader, the choice is yours to do it willingly now, while you still have a choice. Or be forced to do it later, as you suffer the consequences of your rebellion against God.
There will be no second chances for you once that Day has come. I pray you will make Jesus your Messiah, so that you may enter into eternal life today.
God bless you!