I think "blasphemies" is a bit of a strong accusation against someone who holds a different perspective to you.
I think your mistake is in imagining that generational cursing is some major doctrinal theory, when its just a shorthand common sense explanation for what's happening in the spiritual realm.
It simply means that Satan uses any issue from our historic past to gain access and control in our lives.
Without question, the blood of Jesus pays the price for all sin. However, for us to experience that freedom, whenever a falling short or sinful act is exposed, the blood needs to be applied, otherwise Satan can use it to advantage.
We see this in
Rev12v10 And I heard a great voice in heaven, saying, Now is come the salvation, and the power, and the kingdom of our God, and the authority of his Christ: for the accuser of our brethren is cast down, who accuses them before our God day and night. 11And they overcame him because of the blood of the Lamb, and because of the word of their testimony; and they loved not their life even unto death.
The above scripture depicts a court room in the heavenly realm. The chief prosecutor is Satan, God is on the throne, and you are being charged with whatever crimes.
You should know that any claim of innocence or perfection is blown wide open by the utter failure of man's attempts at self perfection is shown Matthew 5. Failure by omission is likewise guilty.
So how do you plead?
John's words explain. We overcome by the blood of the lamb and by proclaiming it.
There is no Fifth amendment, the right to remain silent, in the heavenly court!
Unless we testify to the blood covenant, we will be found guilty and Satan will win.
That truth applies to accusations that have roots in our family history also, as the following example shows.
This occurred long before I ever heard about generational curses.
About 40 years ago, a friend and I were asked to pray for a Christian lady who was visiting our fellowship here in the UK. She didn't give a very clear description of what her problem was or where her need lay.
So we laid it before the Lord and asked for his wisdom. Shortly later, I heard the Lord give the following words, "The spirit of Mormon."
When I told the lady the word, she responded with indignation. She had never been involved with Mormonism, nor even visited their churches. That stumped me a little so I apologised and we stumbled on praying around various things that came to light.
About half an hour afterwards, she suddenly gasped and put her hand over her mouth.
She then related a conversation she had had with her mother when she was a child.
Apparently, in the mid 1800s, her great great great grandfather had gone out to Utah with Brigham Young in his great waggon train to build Salt Lake City for the Mormon Church!
No amount of mental gymnastics would have exposed that spiritual link travelling back over 130 years, had not the Holy Spirit revealed it.
Mormonism is a false doctrine, clearly inspired by demons. Her ancestor had subjected himself to that demon which influenced his spiritual life. That demonic power had travelled down the family line affecting subsequent generations until the day we prayed.
Needless to say, we cast the spirit of Mormonism out of her and set her free from it.
That is the blood of Christ at work.